IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


V 


/, 


4. 

4'^ 


•<°  c^^ 


<  < 


y 


4 


1.0  ;f  iM  iiM 


1.25 


^  !■■  1111122 

^    1^    ill  2-0 


1.4 


lU 


1.6 


^ 
% 


<^ 


/a 


^ 
« 


^1 


Photographic 

Sciences 
Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


4(^ 


'■q^ 


^■^ 


V 


'^ 


^Q> 


^ 


4,s 


4^  # 


f/i 


CIHM/ICMH 
Microfiche 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  Microrep.oductions  /  institut  Canadian  de  microreproductions  historiques 


Technical  and  Bibliographic  Notes/Notes  techniques  et  bibliographiques 


The  Institute  has  attempted  to  obtain  the  best 
original  copy  available  for  filming.  Features  of  this 
copy  which  may  be  bibliographically  unique, 
which  may  alter  any  of  the  images  in  the 
reproduction,  or  which  may  significantly  change 
the  usual  method  of  filming,  are  checked  below. 


D 


D 


D 


D 
D 


D 


D 


Coloured  covers/ 
Couverture  de  couleur 


I      I    Covers  damaged/ 


Couverture  endommagde 


Covers  restored  and/or  laminated/ 
Couverture  restaurde  et/ou  pelliculde 


I      I    Cover  title  missing/ 


Le  titre  de  couverture  manque 


I      I    Coloured  maps/ 


Cartes  gdographiques  en  couleur 

Coloured  ink  (i.e.  other  than  blue  or  black)/ 
Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 


I      I    Coloured  plates  and/or  illustrations/ 


Planches  et/ou  illustrations  en  couleur 

Bound  with  other  material/ 
Relid  avec  d'autres  documents 

Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

Lareliure  serree  peut  causer  de  I'ombre  ou  de  la 
distortion  le  long  de  la  marge  intdrieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text.  Whenever  possible,  these 
have  been  omitted  from  filming/ 
II  se  peut  que  certaines  pages  blanches  ajoutdes 
lors  d'une  restauration  apparaissent  dans  le  texte, 
mais,  lorsque  cela  dtait  possible,  ces  pages  n'ont 
pas  dtd  film^es. 

Additional  comments:/ 
Commentaires  suppldmentaires; 


L'Institut  a  microfilm^  le  meilleur  exemplaire 
qu'il  lui  a  6t6  possible  de  se  procurer.  Les  details 
de  cet  exemplaire  qui  sont  peut-dtre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifier 
une  image  reproduite,  ou  qui  peuvent  exiger  une 
modification  dans  la  mdthode  normale  de  filmage 
sont  indiquds  ci-dessous. 


I      I    Coloured  pages/ 


n 


/ 


D 


This  item  is  filmed  at  the  reduction  ratio  checked  below/ 

Ce  document  est  filmd  au  taux  de  reduction  indiqud  ci-dessous. 


Pages  de  couleur 

Pages  damaged/ 
Pages  endommagdes 


I      I    Pages  restored  and/or  laminated/ 


Pages  restaur^es  et/ou  pellicul6es 

Pages  discoloured,  stained  or  foxei 
Pages  ddcolordes,  tachetdes  ou  piqu^es 

Pages  detached/ 
Pages  ddtachdes 


r~~1    Pages  discoloured,  stained  or  foxed/ 
[~T|    Pages  detached/ 


Showthrough/ 
Transparence 


I      I    Quality  of  print  varies/ 


Quality  indgale  de  I'impression 

Includes  supplementary  material/ 
Comprend  du  materiel  suppl^mentaire 


The 
to  tl 


The 

POS! 
of  tl 
film 


Orig 

begi 

the 

sion 

othe 

first 

sion 

or  il 


□    Only  edition  available/ 
Seule  Edition  disponibia 


Pages  wholly  or  partially  obscured  by  errata 
slips,  tissues,  etc.,  have  been  refilmed  to 
ensure  the  best  possible  image/ 
Les  pages  totalement  ou  partiellement 
obscurcies  par  un  feuillet  d'errata,  une  pelure, 
etc.,  ont  6t6  filmdes  d  nouveau  de  faqon  d 
obtenir  la  meilleure  image  possible. 


The 
shal 
TIM 
whi( 

Map 
diffe 
entir 
begii 
right 
requ 
metl 


10X 

14X 

18X 

22X 

26X 

30X 

T 

12X 

16X 

20X 

24X 

28X 

32X 

The  copy  filmed  here  has  been  reproduced  thanks 
to  the  generosity  of: 

izaak  Walton  Killam  Memorial  Library 
Dalhousie  University 


L'exemplaire  film6  fut  reproduit  grdce  d  la 
g6n6rosit6  de: 

Izaak  Walton  Killam  Memorial  Library 
Dalhousie  University 


The  images  appearing  here  are  the  best  quality 
possible  considering  the  condition  and  legibility 
of  the  original  copy  and  in  keeping  with  the 
filming  contract  specifications. 


Original  copies  in  printed  paper  covers  are  filmed 
beginning  with  the  front  cover  and  ending  on 
the  last  page  with  a  printed  or  illustrated  impres- 
sion, or  the  back  cover  when  appropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
first  page  with  a  printed  or  illustrated  impres- 
sion, and  ending  on  the  last  page  with  a  printed 
or  illustrated  impression. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  — »-  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichever  applies. 


Les  images  suivantes  ont  6t6  reproduites  avec  le 
plus  grand  soin,  compte  tenu  de  la  condition  et 
de  la  nettet6  de  l'exemplaire  film6,  et  en 
conformity  avec  les  conditions  du  contrat  de 
filmage. 

Les  exemplaires  originaux  dont  la  couverture  en 
papier  est  imprimde  sont  film6s  en  commenpant 
par  le  premier  plat  et  en  terminant  soit  par  la 
dernidre  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration,  soit  par  le  second 
plat,  selon  le  cas.  Tous  les  autres  exemplaires 
originaux  sont  filmds  en  commenpant  par  la 
premidre  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  par 
la  dernidre  page  qui  comporte  une  telle 
emprainte. 

Un  des  symboles  suivants  apparattra  sur  la 
dernidre  image  de  cheque  microfiche,  selon  le 
cas:  le  symbol  j  — »>  signifie  "A  SUIVRE",  le 
symbole  V  signifie  "FIN". 


Maps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method: 


Les  cartes,  planches,  tableaux,  etc.,  peuvent  dtre 
film^s  d  des  taux  de  reduction  diffdrents. 
Lorsqu'  le  document  est  trop  grand  pour  dtre 
repr'  en  un  seul  clichd,  il  est  filmd  d  partir 

de  I'an^te  supdrieur  gauche,  de  gauche  d  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  ndcessaire.  Les  diagrammes  suivants 
illustrent  la  mdthode. 


1 

2 

3 

1 

2 

3 

4 

5 

6 

\ 


N 


AN    INTRODUCTORY    LOGIC 


\ 


iSBJ*»*8»>Ji-»«%i4'- 


AN 


(| 


y 


o 


INTRODUCTORY  LOGIC 


BY 


(/ 


JAMES   EDWIN   CREIGHTQN 

SAOE  PROFESSOR  OF   I.OO.C  AND  idFTAPHYS.CS   IN  CORNELL 

UNIVERSITY 


THE   MACMILLAN   COMPANY 

LONDON:  MACMILLAN  &  CO..  Ltd. 
1898 

All  rights  reserved 


M 


0  'i.  ^■^ 


Copyright,  1898, 
By  the  MACMILLAN  COMPANY. 


\\  iSo.  1 
1'.  203,  1 
V.  239.  t 


Noriwooti  ?9ress 

J.  S.  Gushing  &  Co.  —  Berwick  &  Smith 

Norwood  Mass.  U.S.A. 


■    '■*' 


v/sK5;-w»5/Mi*JWis>i:;*»t-*' 


ERRATA 


P.  128,  read  '^  Prosyllogism  "  for  "  Episyllogism."  and  "  Episyl- 

lojiism"  for  "  Frosyllogism,"  throughout. 
P.  180,  hue  II,  for  "is"  read  "are.*' 
P.  203,  Hue  I.  for  "line"  read  "lines." 
P.  239.  for  "  MadgebNig"  read  "  Magdeburg." 


)r 
c 
t 
f 


,->-^    xwi  m 


•A/'"' 


exact  thinkers,  who  attach  a  precise  meaning  to  words 
and  propositions,  and  are  not  imposed  on  by  vague, 
loose,  or  ambiguous  terms."  Although  in  treating  the 
syllogistic  Logic  I  have  followed  to  a  large  extent  the 
ordinary  mode  of  presentation,  I  have  both  here,  and 
when  dealing  with  the  Inductive  Methods,  endeavoured 
to  interpret  the  traditional  doctrines  in  a  philosophical 
way,  and  to  prepare  for  the  theoretical  discussions  of 
the  third  part  of  the  book. 

The  advisability  of  attempting  to  include  a  theory  of 
thought,  or  philosophy  of  knowledge,  even  in  outline, 


?j  X  n^ 


ik 


Norfajooti  i3rfS3 

J.  S.  Cushing  &  Co.  —  Berwick  &  Smith 
Norwood  Masa.  U.S.A. 


:n^f 


PREFACE 


Tins  volume  is  intended  jirimarily  as  a  text-book  for 
colle<;e  students,  and  ^rew  out  of  my  lectures  on  Logic 
to  undergraduate  classes  in  Cornell  University.  It 
aims  at  being  both  practical  and  theoretical.  In  spite  of 
the  obvious  deficiencies  of  formal  Logic  as  a  theory  of 
the  nature  of  thought,  I  am  convinced  that  it  is  one 
of  the  most  valuable  instruments  in  modern  education 
for  promoting  clear  thinking,  and  for  developing  criti- 
cal habits  of  mind.  J.  S.  Mill,  speaking  in  the  Af/fo- 
biograpliy  of  the  discipline  which  he  received  from 
working  logical  exercises,  expresses  the  following 
opinion :  "  I  am  persuaded  that  nothing,  in  modern 
education,  tends  so  much,  when  properly  used,  to  form 
exact  thinkers,  who  attach  a  precise  meaning  to  words 
and  propositions,  and  are  not  imposed  on  by  vague, 
loose,  or  ambiguous  terms."  Although  in  treating  the 
syllogistic  Logic  I  have  followed  to  a  large  extent  the 
ordinary  mode  of  presentation,  I  have  both  here,  and 
when  dealing  with  the  Inductive  Methods,  endeavoured 
to  interpret  the  traditional  doctrines  in  a  philosophical 
way,  and  to  prepare  for  the  theoretical  discussions  of 
the  third  part  of  the  book. 

The  advisability  of  attempting  to  include  a  theory  of 
thought,  or  philosophy  of  knowledge,  even  in  outline, 

V 


VI 


I'RurACt: 


in  an  elementary  course  in  Lojjjic,  may  at  first  si<;ht 
appear  doubtful.  It  seems  to  me,  however,  that  this 
inclusion  is  not  only  justifiable,  but  even  necessary  at 
the  present  time.  Psychology  is  no  lon<;er  a  '  philoso- 
phy of  mind ' ;  but,  under  the  influence  of  experimental 
methods,  has  differentiated  itself  almost  entirely  from 
philosophy,  and  become  a  '  natural '  science.  As  a 
natural  science,  it  is  interested  in  the  structure  of  the 
mental  life,  —  the  characteristics  of  the  elementary 
processes,  and  the  laws  of  their  combination,  —  and 
not  primarily  in  the  function  which  ideas  play  in  giving 
us  knowledge.  It  is  clear  that  p.sychology  does  not 
undertake  to  describe  all  that  mind  is  and  does.  It 
belongs  to  Logic  to  investigate  intelligence  as  a  know- 
ing function,  just  as  it  is  the  task  of  Ethics  to  deal 
with  the  practical  or  active  mental  functions. 

The  practical  question  still  remains  as  to  whether 
this  side  of  Logic  can  be  made  profitable  to  students 
who  have  had  no  previous  philosophical  training.  I 
am  well  aware  of  the  difficulty  of  the  subject,  but  my 
own  experience  leads  me  to  believe  that  the  main  con- 
ceptions of  modern  logical  theory  can  be  rendered 
intelligible  even  to  elementary  classes.  Of  the  incom- 
pleteness and  shortcomings  of  my  treatment  I  am  quite 
conscious ;  but  I  have  endeavoured  to  make  the  matter 
as  simple  and  concrete  as  possible,  and  to  illustrate  it 
by  means  of  familiar  facts  of  experience. 

For  a  number  of  the  practical  questions  and  exer- 
cises, I  am  indebted  to  Professor  Margaret  Washburn 
of  Wells  College ;  others  are  original,  or  have  been 
collected   in   the  course  of   my  reading.      I  have  also 


'    ^ 


fX 


^. 


f 


PKKl'Afl-: 


Vll 


i 


taken  a  number  of  ar<;umL'nts  from  tlic  examination 
papers  of  different  universities,  and  from  various  works 
on  Loi;iL\  especially  from  Jevons's  Studies  in  Dcdnctivi' 
Loi^ic,  from  the  little  volume  entitled  Oin'sdons  on  Loi^ic 
by  Ilolman  and  Irvine  (jd  ed.,  London,  1X97),  and  from 
Ilibben's  [nductivc  Lottie. 

In  writin.i;  the  book,  I  have  been  under  obligation  to 
a  larL;e  number  of  writers  and  books.  My  heaviest 
debt  is  doubtless  to  l^osancpiet,  and  perhaps  next  in 
order  I  am  under  obli;(ations  to  Mill,  Jevons,  Si^svart, 
and  l^radley.  I  have  also  derived  help  from  Minto's 
I.ooicy  Deductive  and  Indnetive^  the  chapter  on  '  Rea- 
sonin.Lc'  in  James's  Principles  of  Psyeho/ot^v,  J.  II.  Ilys- 
lop's  FJeinenis  of  Loi^ic,  and  from  other  works  ti>  which 
reference  is  made  throu£;hout  the  book. 

My  colleagues  in  the  Sage  School  of  Philosophy 
have  kindly  aided  me  from  time  to  time  with  advice 
and  encouragement,  and  I  have  also  received  valuable 
suggestions  from  other  teachers  of  Logic  with  whom  I 
have  talked  and  corresponded.  In  particular,  I  wish 
to  express  my  obligations  to  my  former  colleague,  Pro- 
fessor James  Seth,  who  read  nearly  all  of  the  book  in 
manuscript,  and  to  Ur.  Albert  Lefevre,  who  kindly 
assisted  me  in  reading  the  proofs. 

J.  E.  C. 

CoRNF.LL  University, 
August,  1898. 


'     A 


.a. 


4 


^ 
\ 


^ 


0 

I 


a 


^V 


TABLE    OF   CONTENTS 


Introduction 

CIIAI'J'ER   I 

The  Staxd,,„.n,-  ano  PKom^EM  ok  Luetic 
§  I-     Definition  of  the     ubjcct 
§  2.     I'iclation  to  Psychology  .         .'         ' 
§  3-     logic  as  a  Science  and  an  Art 
§  4-     The  Material  of  Logic 

CHAPTER   II 
Ax  Historical  Sketch  of  Locic 
§5.     The  Logic  of  the  Greeks  :  Aristotle 
I  6.     I-ogic  during  the  Middle  Ages  "         ' 

S  7-     The  Logic  of  Bacon        .  '         '         ' 

§8-    J'Ogic  since  the  Time  of  Bacon       '        .'        " 
Part  I.  _  The  Svllogism 

CHAFFER   III 
The  Syllogism  and  its  Parts 

§9.     The  Nature  of  the  Syllogism 
I  10.     The  Parts  of  the  Syllogism      "         '         '         '         " 
§"•     ^'^^I'-posed  Division  of  Mental  OperaUons'        : 

CHAPTER   IV 
iii^  Various  Kixns  of  Terms 

mg 


I  ^J.     Singulnr.  General,  and  Collective  Tcr 
§  U.     Abstract  and  Concrete  Ter: 


rins 


IX 


i8 

26 
28 
29 


36 
39 

43 


46 
48 


X 


TABLE  OF  CONTENTS 


§  14.     Positive  and  Nej^ative  Terms  . 
§  15.     Absolute  and  Relative  Terms 
§16,     Extension  and  Intension  of  Terms 


PAGE 

54 

55 


§20. 
§  21. 
§  22. 


CHAPTER   V 

Definition  and  Division 


§  17.     Fixing  the  Meaning  of  Terms 
§  18.     Definition       .         .         .         . 
§  19.     Division  .         .         .         . 


CHAPTER   VI 

PKOrOSITIONS 

The  Nature  of  a  Proposition   . 
The  Quality  ana  Quantity  of  Propositions 
Difficulties  in  Classitication 
§  23.     Formal  Relation  of  Subject  and  Predicate 


61 
63 
71 


78 
80 


85 


CHAPTER  VII 

The  Interpretation  ok  Propositions 

§  24.  The  So-called  Pro(     -   >f  Immediate  Inference 

§  25.  The  Opposition  of  .  vtions       .         .         .         . 

§  26.  The  Obversion  of  i^x     js.tior 

§  27.  The  Conversion  of  Propo  ;itions       .         .         .         . 


92 

94 
98 

ICO 


i 


CHAPTER   VIII 

The  Syllogism 

§  28.     The  Nature  of  Syllogistic  Reasoning 
§  29.     The  Rules  of  the  Syllogism     . 
§  30.     The  Figures  of  the  Syllogism 


105 
108 

"3 


CHAPTER  IX 

The  Valid  Moods  and  the  Reduction  of  Figures 

§31.  The  Moods  of  the  Syllogism 115 

§32.  The  Special  Canons  of  the  Four  Figures  .         .         .         -117 

§  2^.  The  Determination  of  the  Valid  Moods  in  Each  of  the  Figures     120 

§  34.  The  Mnemonic  Lines 122 


i. 


i 


PAGE 
52 

54 

55 


61 
63 
71 


78 
So 


85 


92 

94 
98 

ICX) 


105 

108 

"3 


"5 

117 

120 
122 


I 


TABLE  OF  CONTENTS 


xi 


CHAPTER   X 

Abbreviated  and  iHrrc- 
§35.     Enthymen.es  ^  '  "'"'  '''^^^^^  ^^  Aroume^^ 

I  36.     Episyllogisnis  and  iVosvl'l     ■  '         '         "         • 
§37-     Sorites,  or  Chains    Vr^'""'      '         • 
§38.     I-.ularAr^r;;:^^----';^      '         •         •'        .'        .' 

CfiAPTER   XI 

i''--C:;:;;:;;::'''~'""-™.™ 

S40.     Relation  of  Cn/-^'"    "         • 
S-J2.     rheDilcnnia         .  '        •        .        .  ' 

CHAPTER  XII 
§  46.     Material  Fallacies   ■'•••.*'• 

"^'''''•--^^^^--^VK  Methods 
The  p  CFMPTER  xili 

§49.    Explanation    .';•••..■;• 


'•AGE 
126 
127 
129 


136 

'39 

M5 
148 


152 

154 
'57 
'59 


i 


.r  <-'HAPTER   XIV 

^^''•TH0DS0E0,3EKVATlON_p 

„^  f  •     Enumeration  or  Simple  C  '  ""^"''^  ^^  Stahsxics 

§  51.     Statistics  anH  ^f  ?  Counting   . 


172  I 

'76  / 
182  ^ 


/ 


'85 
189 

'94 


'/ 


xii 


,,VBLE  OF  CONTENTS 
CHAriER  XV 

.,,,„,S  __DKTKKMINATI0N   OF   CAUSAL 

,,,      Miirs  Expenmcntanicthocls  .         •         •         '         "         ;         . 
'f;     The  Mctboa  of  Asroemont      .         -  ^         . 

\\l     The  Method  of  Difference       •         • 

ciiArrER  NVl 

.         nviFRMlNA'nON    OF    CAUSAL 

,     1     f  \crrecment  and  Difference     . 

§58'.    The  Method  of  Residues         •         • 

CHAPTER   XVII 

MKXHOUSOFEXVLA^.r.O..-ANAI.OOV 

Explanati^  1^  A^^^y  ^  Explanatory  Hypotheses  • 

Analogy  as  Suggests  ^        ^  Reasoning  ■         • 

The  Incompleteness  of  Analogic. 

CHAPTER  XVHI 

.,       TiiF  Use  of  HYroTiiE 

METHODS   OF   EXPLANATION. -rULU 


PAGE 
198 
200 


209 
211 


iJ 


§59- 
§  60. 
§61. 


219 

223 
226 


;sES 


§62. 

§63- 
§64. 
§65. 


§66. 

§67- 
§68. 

§69. 

§70- 


Reasoning  from  Hypotheses  ^         _ 

The  Formation  of  Hypotheses         •         •         _ 

The  Proof  of  an  Hypothesis    ■         •         ' 
Retirements  of  a  Good  Hypothesis       •        • 

CHAPrER  XIX 

Fvrors  of  Observation     .         •         •  _ 


230 

234 

237 
240 


245 
246 

250 

254 
257 


TAI5LI':   ()1'"   CUNTKNTS 


Xlll 


AGE 
198 
200 


209 
211 
213 


219 

223 
226 


^S  Part  III.  —  The  Nature  of  Thought 

CHAITER   XX 

Judgment  as  tuk  Klkmi^ntakv  Process  of  Tiiofcirr 

§  71.  Thinking  tiic  Process  by  wliicli  Knowledge  grows  or  dcvchjps 

§  72.  Tlie  Law  of  Evolution  and  its  Application  to  Logic 

;  §  73.  Judgment  as  the  Starting-point 

.  ;=         §  74.  Concepts  and  Jutlgnient 

'4  CHAPTER   XXI 

The  Main  Ciiaracterisiics  of  Judgment 

§  75.  The  Universality  of  Judgments        ...... 

§  76.  The  Necessity  of  Judgments   ....... 

§  77.  Judgment  involves  l)Oth  Analysis  and  Synthesis 

§  78.  Judgment  as  constructing  a  System  of  Knowledge 

CHAPTER   XXH 

The  Laws  of  Thought 

§  79,     The  Law  of  Identity 

§  80.     The  Law  of  Contradiction       ....... 

§  81.     The  Law  of  E.xcluded  i\Iiddle  ...... 


PAC-.E 

260 
262 
266 
2C8 


274 
276 
279 
284 


288 

295 
297 


ES 


230 
234 

237 
240 


CHAPTER   XXIII 
Tyi'es  of  JuDG^^■:NT 


§  82.  Judgments  of  Quality 

§  83.  Judgments  of  Quantity    . 

§  84.  Judgments  of  Causal  Connection 

§  85.  Judgments  of  Individuality 


300 
304 
307 
315 


245 

246 

^ 

250 

<    ^ 

.   254 

.  257 

1 

1 

CHAPTER   XXIV 

The  Nature  of  Infekence.  —  Induction  and  Deduction 

§  86.     Judgment  and  Inference 

§  87.     The  Nature  of  Inference 

§  88.     Induction  and  Deduction 


318 
324 
329 


XIV 


TABLE   OF  CONTENTS 


CHAPTER    XXV 

Rational  and  Emmrical  Theories 

§  89.  The  Point  of  View  of  Rationalism  . 

§  90.  The  Doctrine  of  Empiricism    .... 

§  91.  Reasoning  from  Particular  to  Particular 

i  §  92.  Reasoning  from  Particulars  to  a  Universal 


Questions  and  Exercises 


Index 


PAGE 

335 
337 
340 
344 

348 
389 


i:.i 


# 


PAGE 

335 
337 
340 

344 


JNTKODUCTION 

CHAI'TICR   I 

"'  ■"'"~— -...„  o,  ,„,,^ 

«'■  Definition  of  the  Subject       r      • 
-^  the  science  of  though/or  ~  ^h"^" -""'^  "^^ '^""-^^ 
vost'Sates  the  process  of  t'h  „k L"  V""  '''''''  '"- 
"  "  Senerai  way  at   least   Sf  •    ^'""^  ""'  ''"°>^«. 

°f  «s  l^eculiaritics.     Thinking  •    .?'   ""«"°"s'y  some 
—  of  Which  knowh^  '  "°:  "  f:-  '"'^"^^'"^'  -'  h  . 
-^"y /■«..„  any  fact  untl  we  If"""^"-     ^^  ^o   "ol 

-'»  -^-Perience,  and'th  s  e  i""  '"  '''  "''^  ''"'^  "^ 

''■'^'  "^as  con,e  to  us  ^     tr         '^'"P''^'  ''«-- 
conch,sions  which  we  havefel    '77  "■■  ''^^'■■^^^'  «"d 
;-=•     'J  have  W.,.  we      y"tf ;'  T  """  "^'"'^- 
I  do  not  ^v.«e,  it.-     That  ^^    ..      f  "  '''''^°"<^^t-  b« 
-'-''^"ed  as  a  resnit  of  o'r  oln   tl  '^  •'   "''  "°'  •"^- 
''"efore  claim  the  title  o    kn  T^'"''  '""  ^^"""t 

hand,  that  the  earth  is  rouLf T        °"'^-     °"  "^'^  °'her 
--^  fo^  an  educated  :;  7,1  \  -^  "--  of 
'"^.^^,  because  it  is  a  conch^in        u         ^'''^'^  "'  ^»^«'- 

himself  •>  P""'"S  '"gether  various  facts  for 


THE   STANDPOINT   AND    PROBLEM   OF   LOGIC 


f 


Logic,  then,  in  dealing  with  thinking,  is  concerned 
with  the  process  by  which  knowledge  is  obtained.  In 
defining  it  as  a  science,  we  mean  that  it  seeks  to  sub- 
stitute exact  and  systematic  knowledge  regarding  the 
nature  of  thought  for  the  popular  notions  to  be  found 
in  everyday  life.  Like  all  the  sciences,  logic  has  to 
correct  and  supplement  ordinary  knowledge.  It  is  its 
mission  to  help  us  to  understand  more  exactly  and 
completely  the  way  in  which  thinking  goes  on,  and 
to  discover  the  laws  which  are  followed  in  gaining 
knowledge. 

But  it  is  also  the  business  of  a  science  to  system- 
atize facts.  Logic,  then,  cannot  content  itself  with  a 
mere  description  of  this  or  that  kind  of  thinking,  in 
isolation  from  other  ways  in  which  we  think.  It  must 
also  deal  with  the  way  in  which  the  various  kinds  of 
thinking  are  related.  For  example,  we  apply  such 
terms  as  'conception,'  'judgment,'  'induction,'  and  'de- 
duction '  to  different  intellectual  operations,  and  give 
the  distinguishing  characteristic  in  each  case.  But  it  is 
necessary  as  well  to  understand  how  these  processes 
are  related.  Since  all  thinking  has  one  end,  the  dis- 
covery of  truth,  the  various  intellectual  operations  must 
mutually  cooperate  and  assist  in  this  result.  All  of 
the  logical  processes,  then,  stand  in  relation  to  one 
another.  They  are  all  parts  of  the  one  intelligence, 
though  they  may  well  represent  different  stages  or 
steps  in  its  work  of  obtaining  knowledge.  It  becomes 
the  business  of  logic,  then,  to  show  us  the  organic 
structure  of  thought.  In  other  words,  it  must  furnish 
a  comprehensive  view  of  the  way  in  which  intelligence 


1 


§  I.     DEI'INITION   OK    THE  SUHJIXI' 


iccrncd    - 
cd.     In 

to  sub- 
ling  the 
,e  found 
:  has  to 

It  is  its 
ctly  and 

on,  and 

gaining 

3  system- 
If  with  a 
nking,  in 
It  must 
,  kinds  of 
)ply   such 
'  and  *de- 
and  give 
But  it  is 
processes 
i,  the  dis- 
tions  must 
t.      All  of 
on  to  one 
telligence, 
stages   or 
t  becomes 

le  oi;gani? 
ust  furnish 
ntelligence 


acts,   and   the   part  which   processes  like   'conception,' 
'judgment,'  'induction,'  etc.,  play. 

(i)  The  word  •I();,mc'  is  derived  from  the  adjective  corre.spondin<^ 
to  the  (Ireek  noun  Aoyos,  wiiicli  signifies  either  a  complete  thou^lit, 
or  a  word  as  the  expression  of  that  tiiouj^ijht.  Tlie  sinsfular  form  of 
the  adjective  AoyiKr/,  from  which  the  English  word  is  derived,  was 
supposed  tf)  qualify  either  ima-Tr'nir)  as  apjilying  to  the  theoretical 
science  of  logic,  or  rix^t]  as  referring  to  the  ])ractical  application 
of  its  rules  and  as  affording  guidance  in  the  art  of  correct  reason- 
ing. We  shall  have  to  raise  the  (luestion  in  a  subsequent  section 
how  far  it  is  possible  to  reg  d  logic  as  an  art,  or  a  system  of  rules 
which  teacli  us  how  to  reason  correctly. 

(2)  We  have  defined  logic  as  the  science  of  tlic  operations  and 
processes  of  thought,  or  as  the  science  of  thinking.  It  is  evident, 
however,  that  tliis  definition  does  not  carry  us  very  far  unless  we 
know  what  thinking  means.  And  to  gain  a  clearer  idea  of  this  com- 
mon term  may  be  said  to  be  the  problem  of  logic.  This  is,  however, 
by  no  means  as  easy  a  task  as  may  at  first  appear.  Familiar  words 
and  phrases  often  conceal  difficulties.  They  are  constantly  repeated 
without  reflection,  and  this  very  frequency  of  repetition  is  likely 
to  prevent  us  from  trying  to  gain  any  clear  ideas  regarding  the 
nature  of  the  objects  which  they  denote.  It  is  only  when  we 
become  discontented  with  our  knowledge  regarding  any  subject, 
when  doubts  arise  whether  we  really  understand  the  meaning  of 
the  words  which  we  use,  that  we  attempt  to  make  our  knowledge 
scientific,  i.e.,  to  gain  clear,  definite,  and  systematic  ideas.  This 
can  perhaps  be  made  cleatev  by  considering  the  main  differences 
between  an  educated  and  an  uneducated  man.  The  educated  man 
has,  of  course,  a  great  deal  more  information  than  the  other,  and 
his  knowledge  is  more  definite  and  systematic.  But  a  second  and 
more  important  distinction  is  found  in  the  attitude  of  mind  which 
education  begets.  The  educated  man  is  desirous  of  knowing  more, 
because  he  is  sensible  of  his  own  ignorance.  The  uneducated 
man,  on  the  other  hand,  supposes  that  he  knows  all  about  things 
whose  names  are  familiar  to  him.  He  can  settle  puzzling  theo- 
logical   or   political    problem^    off-hand   in    a    way    which    is   per- 


1 


11  IK   STANDroiNT   AND   I'ROBLEM    OK   LOGIC 


» . 


'T 


I 


fectly   satisfactory  tu   liiniscit,  without  study,  ;iiul  almost  without 
reflection. 

It  is  clear  that  no  intellectual  salvation  is  possible  for  a  man  so 
lont;  as  he  remains  in  this  state  of  mind.  A  sense  of  one's  own 
ignorance  is  the  bej^inning  of  wisdom.  Socrates,  one  of  'he  great 
pioneers  of  science  among  the  CIreeks,  and  especially  of  the  sciences 
of  logic  and  etiiics,  was  so  hrmls  convinced  of  this  that  he  made  it 
the  business  of  liis  life  to  go  about  the  streets  of  Athens  and  con- 
vince those  "who  thought  they  were  wise  and  were  not  wise,"  of 
their  ignorance.  '*  And  because  I  did  this,'"  he  says  naively,  "  many 
of  them  were  angry,  and  became  my  enemies." 

§  2.  Relation  to  Psychology.  —  It  may  aid  us  in 
obtaining  a  clearer  view  of  what  thinking  is,  if  we 
compare  the  general  standpoint  of  logic  with  that  of 
psychology.  Both  of  these  sciences  deal  with  what 
goes  on  in  mind  or  consciousness,  and  are  thus  opposed 
to  the  so-called  objective  sciences,  which  are  all  con- 
cerned with  some  group  or  field  of  external  facts.  But 
in  spite  of  this  agreement,  there  is  an  important  dis- 
tinction between  logic  and  psychology.  In  the  first 
place,  ([3sychology  deals  with  all  that  there  is  in  mindj 
It  describes  pleasures  and  pains,  acts  of  will,  and  the 
association  of  ideas,  as  well  as  what  is  usually  called 
logical  thinking.  But  logic  does  not  differ  from  psy- 
chology simply  by  being  less  inclusive  than  the  latter. 
It  is  true  that,  from  the  standpoint  of  psychology,  the 
thought-process  is  merely  a  part  of  the  mental  content, 
which  has  to  be  analyzed  and  described  like  anything 
else  which  goes  on  in  consciousness.  Thinking  has 
doubtless  for  psychology  peculiar  marks  or  charac- 
teristics which  distinguish  it  from  other  related  pro- 
cesses like  those  of  association;  but  when  these  have 


§  2.     Ri:i-ATION  TO   rSYCIIOLOClY  5 

been  found,  and  the  psycholoj^ical  descrijition  of  think- 
in^^  is  complete,  the  question  with  which  lo<;ic  deals  has 
not  yet  been  raised.  For  loj^ic,  as  we  shall  see  i)res- 
cntly,  adopts  a  different  standpoint,  and  investigates 
with  a  different  end  in  view. 

The  important  difference  is  this:  In  psychology  we 
are  interested  in  the  content  of  consciousness  for  its 
07011  sa/cc.  and  just  as  it  stands.  We  try  to  find  out 
what  actually  goes  on  in  our  minds,  and  to  describe  it 
just  as  we  should  any  event  which  occurs  in  the  exter- 
nal world.  But  in  logic  the  question  is  not :  What  are 
mental  processes }  but  rather :  What  knowledge  do 
they  give  us,  and  is  this  knowledge  true  or  false .'' 
Logic,  in  other  words,  does  nj)^  regard  the  way  in 
which  ideas  exist,  and  is  not  interested  in  them  for 
ivJiat  tJicy  arc,  but  ratherJxLthe  purpose  which  they  sub- 


serve in  affording  us  knowledge  of  something  bevond 
.thcmselyes.  Psychology,  in  its  description  of  conscious 
states,  inquires  regarding  their  quality,  intensity,  dura- 
tion, etc.,  and  the  ways  in  which  they  combine  with 
each  other  to  form  complex  ideas.  The  problem  with 
which  logic  is  concerned,  on  the  other  hand,  has  refer- 
ence to  the  value  of  ideas  when  they  are  taken  to 
represent  facts  in  the  real  world.  In  other  words,  the 
question  which  logic  raises  is  not  regarding  the  actual 
character  of  ideas  as  existing  processes,  but  regarding 
their  value  or  significance  as  pieces  of  knowledge. 

(i)  The  relation  between  logic  and  psychology  may  perhaps  be 
illustrated  by  referring  to  that  which   exists  between   morphology 
and  physiology.     Morphology  deals  with  the  form  and  structure  '' 
of  living  organisms,  and  physiology  with  the  various  acts  and  func- 


■IIIK    Si  ANDPOIM-    AM)    TKoliLKM    ()!•    FXKilC 


.t 


I       i 


)l 


tioiis  which  thisi'  oi^aiiisius  (li.sch;irjj;r.  'I'luis  \vc  speak  of  the 
former  as  the  si  iciicc  of  form  or  structure,  aiul  of  the  latter  as  tlie 
science  of  funciion.  In  the  same  way.  psycholo;^;)'  may  l^e  said  to 
(leal  with  the  actiial  structure  of  mental  processes,  and  logic  with 
the  part  which  they  play  in  giving  us  kimwledgc 

It  must  i)e  noticed,  however,  that  this  is  a  distinction  made  for 
purposes  of  investi^^ation,  and  does  not  denote  that  structure  and 
function  have  nothing  to  do  with  each  other.  On  the  contrary, 
some  knowled^^e  of  the  function  is  often  necessary  in  order  to  under- 
stand the  structure  of  an  or^an  ;  and,  on  the  other  hand,  it  is  usually 
true  that  the  nature  of  a  function  only  becomes  completely  intelligi- 
ble when  the  character  of  the  mechanise  with  which  it  works  is 
known.  And  the  same  holds  true,  I  think,  of  the  relations  between 
psychology  and  logic.  Although  it  has  bev n  found  profitable  when 
dealing  with  consciousness,  as  in  the  biological  realm,  to  investigate 
the  nature  of  structure  and  function  separately,  yet  here,  as  there, 
the  two  lines  of  inquiry  cross  each  other;  for  it  is  beyond  question 
that  the  knowledge  we  obtain  by  thinking  is  largely  dependent  upon 
the  character  (quality,  intensity,  etc. )  of  the  actual  processes  in  con- 
sciousness. To  understand  the  nature  of  a  logical  idea,  then,  it  is 
often  necessary  to  refer  to  the  psychological  facts  and  their  actual 
mode  of  behaviour.  And  it  is  equally  true  that  one  cannot  carry 
on  a  psychological  investigation  into  the  nature  of  mental  processes 
without  taking  account,  to  some  e.xtent,  of  the  part  which  they  play 
in  giving  us  knowledge.  No  psychology  is  able  to  take  ideas  simply 
as  existing  conscious  processes  to  which  no  further  meaning  or 
importance  attaches  ;  it  is  only  with  reference  to  the  function  they 
perform  as  kmnviug  states  that  their  own  peculiar  character  can  be 
understood.  In  other  words,  the  intellectual  activities  and  purposes 
of  mind  must  be  presupposed  in  psychology,  though  this  science,  for 
the  most  part,  goes  its  way  as  if  the  ideas  were  not  cognitive  at  all. 
At  least  this  seems  to  be  true  of  the  'new'  or  experimental  psy- 
chology as  opposed  to  the  philosophies  of  mind. 

(2)  It  would  of  course  be  presumptuous,  as  well  as  utterly  useless, 
for  any  writer  to  draw  a  hard  and  fast  line  between  logic  and  psy- 
chology, and  to  forbid  others  to  overstep  it.     In  attempting  to  dis- 


% 


Lilt' 


§2.     UKI-AIION    TO   l'SV(:il()L()(iY 


leak  of  the 

after  as  (lie 

■  1^1'  said  to 

'•»Mic  with 

'1  made  for 
iictiirc  and 
2  contrary, 
'■  to  undcr- 
it  is  usually 
ly  intcHi^d- 
t  works  is 
IS  I)etween 
able  when 
nvestigate 
<  as  there, 
I  question 
lent  upon 
2s  in  con- 
hen,  it  is 

ir  actual 
lot  carry 

rocesses 

ley  play 

s  simply 
ming  or 

on  they 
can  be 

urposes 

nee,  for 

2  at  all. 

al  psy- 

iseless, 
d  psy- 
to  dis- 


cover the  dividing  line  between  two  closely  related  sciences  one 
must  be  j^uided  by  the  procedure  of  those  who  are  workiu';  in  the 
fields  which  it  is  proposed  to  divide.  Now,  it  must  be  admitted  that 
bv  HI)  means  all  of  the  recent  writers  in  psychology  limit  the  sphere 
of  their  science  in  the  way  above  described  ;  tiiat  is,  th"re  are 
certain  psychologists  who  do  not  conline  their  attention  to  the  mere 
mental  i^rocesses  as  such,  but  include  in  tluir  investigations  the  fur- 
ther problem  regarding  the  part  which  these  processes  play  in  giving 
us  knowledge.  Thus  in  Vvoicssov  jiimvs's  /'////( /p/rs  (>/  /\vi/i(>/i%y 
there  is  an  excellent  chapter  on  *  Reasoning"  which  certaiidy  ct)n- 
tains  as  much  logical  as  psychological  matter.  In  the  same  way. 
one  finds  problems  of  knowledge  discussed  in  the  psychological 
writings  of  Professor  Ladd,  and  also,  to  some  extent,  in  the  ncent 
work  by  Mr.  Stout  entitled  Aiialyii'i  /\V(/iolt\i:[Y.  In  spite  of  tiiis, 
it  is  evident  that  the  tendency  of  the  'new,'  or  laboratory  i)sy- 
chology,  is  towards  a  sharper  differentiation  of  its  problems  from 
those  of  logic.  The 'natural  science  of  psychology  '  is  interested 
in  the  conscious  process  as  an  event  in  time  with  certain  defi- 
nitely ascertainable  characteristics.  It  is  perhaps  not  a  matter  of 
great  moment  whether  the  name  'psychology'  be  limited  to  this 
kind  of  incpiiry,  or  whether  philosophical  iiupiiries  regarding  the 
nature  of  knowledge  be  also  included  under  it.  I  have  assumed, 
however,  in  this  section,  that  psychology  is  now  being  differentiated 
from  the  more  general  inquiries  regarding  th?  nature  of  mind,  and 
that  it  has  taken  for  its  field  of  investigation  the  nature  of  mental 
processes  regarded  merely  as  mental  processes. 

Consider  a  little  further  the  nature  of  the  idea.s  with 
which  logic  deals.  Every  idea,  as  we  have  seen,  not 
only  exists  in  some  definite  fashion  in  some  particular 
consciousness,  connected  with  certain  other  ideas,  and 
with  a  definite  quality,  intensity,  etc.,  but  it  has  a  mean- 
ing  or  significance  as  a  piece  of  knowledge.  It  not 
only  is  something,  but  it  also  stands  for  or  si]<f/iijifs 
something.     Now  it  is  not  with  the  existence,  but  with 


■i 


8 


THE   STANDPOINT   AND   PROBLEM   OF   LOGIC 


the  meaning   side  of   ideas    that   logic   has  to  do. 


A 


i 


; 


logical  idea,  or  piece  of  knowledge,  is  not  merely  a 
modification  of  consciousness  which  exists  in  the  mind 
of  some  individual  at  a  particular  time.  For  example, 
the  proposition  :  *  The  three  angles  of  a  triangle  arc 
equal  to  two  right  angles,'  will  give  rise  to  a  number 
of  definite  psychological  processes  (probably  auditory 
or  visual  in  character)  in  the  mind  of  any  individual. 
These  processes  would  also  probably  differ  in  character 
in  the  case  of  two  persons.  The  meaning  of  the  propo- 
sition, however,  is  distinct  from  the  definite  processes 
which  arise  in  particular  minds.  The  proposition  has 
a  significance  as  an  objective  fact,  or  piece  of  know- 
ledge, outside  my  mind ;  the  psychological  images  or 
processes  may  differ  for  different  persons,  but  the  fact 
expressed  is  the  same  for  all  minds  and  at  all  times. 


'     { 


/■ '( 


§  3.  Logic  as  a  Science  and  an  Art. — We  have  de- 
fined logic  as  the  science  of  thought,  but  it  has  often 
been  pointed  out  that  there  are  equally  strong  reasons 
for  considering  it  to  be  an  art.  Jevons  makes  the 
distinction  between  a  science  and  an  art  very  clear  by 
saying  that  "  a  science  teaches  us  to  know,  and  an  art 
to  do."  A  science  is  interested  in  the  discovery  of  facts 
and  laws  without  any  thought  of  what  use  may  be  made 
of  this  knowledge ;  an  art,  on  the  contrary,  gives  practi- 
cal guidance  and  direction  for  some  course  of  action. 
The  question  before  us,  then,  is  this :  Does  logic  merely 
give  us  knowledge  about  the  ways  in  which  we  think, 
or  does  it  also  help  us  to  think  rightly } 

Before  we  attempt  to  answer  this  question,  we  must 


)GIC 

to  do.     A 
merely  a 
the  mind 
■  example, 
angle  are 
a  number 
auditory 
Klividual. 
character 
ic  pro])o- 
:>rocesses 
ition  has 
)f  know- 
lages  or 
the  fact 
nes. 

ave  de- 
s  often 
reasons 
:cs  the 
ear  by 
an  art 
f  facts 
made 
3racti- 
ction. 
I c rely 
:hink, 

must 


§  3.    LOGIC  AS   A   SCIENCE  AND  AN   ART  9 

note  that  practical  rules  of  action  are  based  upon  sci- 
entific knowledge.  An  art,  in  other  words,  depends 
upon  science,  and  grows  in  perfection  with  the  advance 
of  scientific  knowledge.  Thus  medicine,  as  the  art  of 
healing,  is  founded  upon  the  sciences  of  chemistry, 
physiology,  and  anatomy,  and  it  is  because  of  the  great 
dis<;ovcries  which^have  been  made  in  these  fields  within 
recent  years,  that  it  has  been  able  to  advance  with  such 
gigantic  strides.  Again,  the  art  of  singing,  in  so  far  as 
it  is  an  art  which  can  be  taught  and  learned,  depends 
upon  a  knowledge  of  the  physical  and  physiological 
laws  of  the  vocal  organs.  An  art,  then,  always  pre- 
supposes a  certain  amount  of  science,  or  knowledge, 
and  is  simply  the  application  of  this  knowledge  to  some 
practical  purpose.  In  some  cases  the  application  is 
very  obvious  and  direct ;  in  others,  it  is  much  more 
difficult  to  determine ;  but,  in  general,  there  is  always 
this  relation  between  theory  and  practice,  between 
knowing  and  doing. 

From  what  has  been  already  said,  it  will  be  evident 
that  logic  must  first  be  a  science  before  it  can  become 
an  art.  Its  first  business  must  be  to  investigate  the 
nature  of  thought,  and  t6  attempt  to  discover  the  differ- 
ent forms  which  the  latter  assumes  in  the^course  of  its 
development.  So  that  we  were  right  in  defining  it  as 
primarily  a  science.  But  the  further  question  remains : 
How  far  is  it  possible  to  apply  the  laws  of  logic  after 
they  have  been  discovered  in  such  a  way  as  to  obtain 
directions  how  to  reason  correctly  in  every  case .''  Can 
we  not  apply  our  knowledge  of  the  laws  of  thought  in 
such  a  way  as  to  get  a  complete  art  of  reasoning,  just  as 


i 


10 


THE   STANDPOINT   AND   PROBLEM   OF   LOGIC 


)1   i 


the  laws  of  chemistry  and  biology  arc  applied  in  medi- 
cine ? 

It  is  no  doubt  true  in  logic,  as  everywhere,  that  scien- 
tific knowledge  is  capable  of  practical  application.  But 
I  do  not  think  that  logic  can  be  regarded  as  an  art,  in 
the  sense  that  it  furnishes  a  definite  set  of  rules  for 
thinking  correctly.  There  is  an  important  distinction 
in  this  case  which  must  not  be  left  out  of  account.  The 
physical,  and  even  the  biological  sciences,  deal  with 
things  whose  way  of  acting  is  perfectly  definite  and 
uniform.  The  character  of  any  of  the  physiological 
functions,  as,  e.g.,  digestion,  may  be  comparatively  com- 
plex and  difficult  to  determine,  but  it  always  attains  its 
end  through  the  use  of  the  same  means.  When  once  its 
laws  are  understood,  it  is  not  difficult  to  prescribe  just 
how  the  proper  means  may  always  be  secured  for  the 
attainment  of  the  desired  end.  But  thinking  has  much 
more  flexibility  in  its  way  of  acting.  We  cannot  say 
with  the  same  definiteness  as  in  the  cases  we  have  been 
considering,  that  in  order  to  reach  a  certain  end  we  must 
use  a  definite  set  of  means.  It  is  not  possible,  that  is, 
to  say:  If  you  would  learn  what  is  true  about  this  sub- 
ject, you  must  follow  this  rule  and  that  in  your  thinking. 
Logic,  it  seems  to  me,  cannot  be  regarded  as  an  art  like 
photography,  or  even  like  medicine  ;  for  it  is  not  possible 
to  lay  down  definite  rules  for  the  guidance  of  thinking 
in  every  case.  What  we  can  do,  is  to  show  the  method 
by  which  new  truths  have  been  discovered,  and  the 
general  conditions  which  must  always  be  fulfilled  in 
reasoning  correctly.  And  it  is  also  possible  to  point 
out  the  m.ore  common  errors  which  arise  when  these 


I 


IC 


§  3.     LOGIC  AS  A   SCIENCE  AND   AN   ART 


II 


in  medi- 

lat  scien- 
311.      But 
.n  art,  in 
ules  for 
stinction 
It.     The 
eal  with 
lite   and 
iological 
sly  coRi- 
tains  its 
once  its 
:ibe  just 
for  the 
LS  much 
not  say 
/e  been 
^e  must 
that  is, 
is  sub- 
inking, 
irt  like 
ossible 
inking 
lethod 
id  the 
ed   in 
point 
these 


1 


conditions  are  violated.  I^ut  it  is  beyond  the  power  of 
logic  to  formukite  any  definite  set  of  rules  for  the 
guidance  of  thinking  in  every  case. 

We  have  found  that  we  must  give  up  all  extravagant  hopes 
of  the  practical  advantages  to  be  gained  from  a  study  of  logic. 
There  is  no  set  of  rules  which  will  make  us  infallible  reasoners. 
That  being  admitted,  the  question  may  be  raised  as  to  the  utility  of 
the  study.  What  will  it  profit  us  to  devote  ourselves  to  this  subject? 
It  might  be  a  sufiicient  answer  to  ooint  out  that  this  question  pre- 
supposes that  knowledge  has  always  some  ulterior  motive.  The 
assumption  upon  which  it  is  based  is,  in  other  words,  that  the  prac- 
tical advantages  arising  from  any  study  furnish  the  only  justification 
for  undertaking  it.  But  it  is  scarcely  necessary  to  say  that  this  is  not 
an  attitude  which  any  student  should  adopt.  A  student?is  one  who 
prosecutes  a  study  for  its  own  sake,  with  no  other  motive  than  the 
desire  to  know.  And  to  such  a  person  logic  should  not  be  without 
interest.  For  as  we  have  seen,  it  is  an  inquiry  into  the  nature  of 
intelligence.  Its  results,  therefore,  are  not  in  themselves  less  in- 
teresting or  less  important  than  a  knowledge  of  the  various  forms 
of  geological  formation,  or  of  plant  or  animal  life.  "  If  it  is  re- 
garded as  a  valuablea^hievement,"  says  Hegel,  "to  have  discovered 
sixty  odd  species  of  parrot,  a  hundred  and  thirty-seven  species  of 
veronica,  and  so  forth,  it  should  surely  be  held  a  far  more  valuable 
achievement  to  discover  the  forms  of  reason."^ 

The  necessity  of  devoting  oneself  to  a  science  quite 
unselfishly  cannot  be  too  strongly  enjoined,  nor  the  evils 
which  arise  when  one  begins  a  study  greedy  '  for  quick 
returns  of  profit,'  too  often  emphasized.  Nevertheless, 
since  the  question  has  been  raised,  it  would  not  be  just 
to  refuse  altogether  to  speak  of  the  particular  results 

1  Hegel,  IVerke,  Bd.  V.,  p.  139.  Quoted  by  Bosanquet  at  the  beginning 
of  his  work  on  Logic. 


1 


12 


THE   STANDPOINT   AND   PROBLEM   OF   LOGIC 


i 


li 


I 


1 


arising  from  a  study  of  logic.  As  we  have  seen,  we 
cannot  hope  to  become  infalHble  reasoners  by  its  aid. 
It  is  just  as  true  here  as  in  any  other  field,  however, 
that  knowledge  is  power,  and  ignorance  synonymous 
with  weakness.  For  even  if  one  resolves  never  to  look 
inside  a  logic  book,  one  must  nevertheless  have  some 
theory,  or  act  upon  some  principle  —  it  may  be  quite 
unconsciously  —  in  deciding  what  is  true  and  what  is 
false.  For  instance,  a  man  may  act  upon  the  principles 
that  those  things  are  likely  to  be  true  which  are  favour- 
able to  his  own  interests,  or  which  agree  with  his  own 
prejudices,  or  with  the  articles  of  his  church  or  political 
party.  Or  again,  he  may  regard  his  senses  as  the 
standards  of  truth.  Mr,  Bradley  says  that  if  dogs 
reason,  they  proceed  upon  the  principle,  'what  smells, 
exists,  and  what  does  not  smell  docs  not  jxist.'  It  is  not 
uncommon  to  hear  it  announced  :  What  can  be  perceived 
through  the  senses  is  true ;  what  cannot  be  sensed,  or  is 
contrary  to  the  testimony  of  the  senses,  is  an  absurdity. 
This  was  the  standard  of  truth  adopted,  for  example,  by 
those  who  attempted  to  overthrow  the  Copernican  theory 
by  declaring  it  to  be  in  plain  contradiction  to  the  tes- 
timony of  the  senses. 

It  seems  evident,  therefore,  that  intellectual  beings 
cannot  escape  some  kind  of  logical  theory,  whether  they 
hold  it  consciously  or  unconsciously.  It  is  clear,  too, 
that  the  character  of  this  theory  will  determine  to  a 
great  extent  their  thoughts  and  opinions.  The  only 
question  which  remains  is  whether  it  is  better  to 
leave  this  matter  entirely  to  chance,  or  to  attempt  to 
gain  some  clear  ideas  regarding  the  nature  of  thinking. 


GIC 


§4.    THE   MATERIAL  OF   LOGIC 


13 


seen,  we 
)y  its  aid. 

however, 
lonymous 
er  to  look 
ave  some 

be  quite 
3  what  is 
principles 
*e  favoiir- 

his  own 
r  political 
:s  as  the 

if  dof^s 
It  smells,.-' 

It  is  not 
)erceived 
sed,  or  is 
bsurdity. 
mplc,  by 
n  theory 


and  the  conditions  under  which  knowledge  arises.  It 
can  scarcely  be  doubted  that,  even  from  a  practical  point 
of  vie.v,  a  true  theory  is  better  than  a  false  one.  A 
man  who  has  reflected  upon  the  nature  of  proof,  and  the 
principles  of  reasoning,  is  much  less  likely  to  be  deceived 
than  one  who  is  guided  ui»consciously  by  assumptions 
which  he  has  never  examined.  It  is  always  an  advan- 
tage to  know  exactly  the  nature  of  the  result  at  which 
we  are  aiming,  and  to  be  perfectly  clear  as  to  our  own 
purposes.  And  this  is  just  what  a  study  of  logic  aids 
us  in  attaining.  It  helps  us  to  understand  the  structure 
of  knowledge  and  conditions  of  proof.  Moreover,  it 
engenders  the  habit  of  criticising  propositions,  and  ex- 
amining the  evidence  upon  which  they  rest.  Further, 
the  importance  of  this  study  for  a  theory  of  education 
may  well  be  emphasized.  For  education,  at  least  so 
far  as  it  undertakes  to  train  the  knowing  powers  of 
the  individual,  must  be  based  upon  a  knowledge  of  the 
necessary  laws  of  intelligence,  and  of  the  steps  or  stages 
which  it  passes  through  in  its  process  of  development. 

§  4.  The  Material  of  Logic — The  business  of  logic, 
as  we  have  seen,  is  to  discover  the  laws  of  thought  and 
to  show  the  differences  which  exist  between  real  and 
imaginary  knowledge.  Where  now  shall  we  find  the 
materials  for  this  study .''  Where  are  the  facts  which 
are  to  be  taken  as  a  starting-point .''  It  is,  of  course, 
impossible  to  learn  directly  from  one's  own  conscious- 
ness all  that  thinking  is,  or  everything  of  which  it  is 
capable.  For,  quite  apart  from  the  difficulty  of  observ- 
ing the  process  of  thought  while  it  is  actually  going  on, 


14 


THE   STANDrOIXr   AND    I'RODLEM   OF   LOCJIC 


I 


no  one  can  suppose  that  his  own  mind  furnishes  an 
example  of  all  that  thinking  has  done,  or  can  do.  It  is 
necessary  to  take  a  broader  view,  and  learn  how  other 
men  think.  Of  course,  we  cannot  look  into  the  con- 
sciousness of  other  men,  but  we  can  study  the  products 
and  results  of  their  thoughts.  The  history  of  the  way 
in  which  truth  has  been  discovered  is  of  the  greatest 
importance  for  logic.  It  must  not  be  forgotten  that 
thought  is  not  a  thing  which  can  be  described  once  for 
al).  It  is  rather  a  living  activity,  which  is  constantly 
showing  what  it  is  in  what  it  does.  The  history  of  the 
various  sciences  furnishes  a  record  of  the  steps  by  means 
of  which  thought  has  built  up  knowledge.  And,  in  this 
record,  we  have  also  a  revelation  of  the  nature  of  the 
thinking  process  itself,  and  of  the  stages  through  which 
it  has  passed  in  the  course  of  its  development. 

It  is  by  a  reflection,  then,  upon  the  nature  of  proposi- 
tions which  are  universally  regarded  as  true  that  the 
laws  of  logic  are  obtained.  There  is  always  a  permanent 
body  of  knowledge  which  no  one  thinks  of  calling  in 
question.  Both  in  everyday  knowledge,  and  in  the 
sciences,  there  is  always  found  a  great  number  of  propo- 
sitions which  appear  true  to  everybody.  And  it  is  here 
that  logic  finds  its  material.  Taking  the  facts  and  propo- 
sitions which  are  recognized  as  certain  by  everybody, 
logic  examines  their  structure  in  order  to  learn  about 
the  nature  of  the  intellectual  processes  by  which  they 
have  been  discovered.  What  principles,  it  asks,  are 
involved  in  those  pieces  of  knowledge,  and  what  partic- 
ular acts  of  thought  were  necessary  to  discover  them  } 
It  is   only  by  examining  various  pieces  of  knowledge 


k;ic 

rnishes  an 
do.     It  is 
how  other 
3  the  con- 
z  products 
f  the  way 
e  greatest 
3tten   that 
1  once  for 
:onstantly 
)ry  of  the 
by  means 
id,  in  this 
re  of  the 
gh  which 

^roposi- 
:hat  the 
rmanent 
illing  in 
in   the 
propo- 
is  here 
propo- 
rybody, 
about 
::h  they 
<.s,   are 
partic- 
them  ? 
kvledge 


§  4.    THE   MATERIAL  OF  LOGIC 


15 


1. 


I. 


1 


in  this  way,  and  attempting  to  trace  out  the  conditions 
of  their  discovery,  that  one  can  learn  anything  new 
regarding  the  hiws  and  character  of  thought.  In  other 
words,  there  is  no  way  of  learning  about  thinking  ex- 
cept by  studying  what  it  has  done.  The  best  way  of 
getting  information  about  what  thought  can  do,  is  to 
study  what  it  has  already  accomplished. 

Every  piece  of  knowledge,  as  tlie  product  of  thinking,  is  to  some 
extent  a  revelation  of  the  nature  of  intelligence.  But  scientific 
knowledge  —  by  this  I  mean  the  results  of  the  philosophical  and 
historical  sciences  as  well  as  of  the  so-called  natural  sciences  — 
exhibits  perhaps  most  clearly  the  nature  of  thought.  For  the 
history  of  these  sciences  enables  us  to  see  the  process  of  know- 
ledge, as  it  were,  in  the  making.  In  tracing  the  history  of  philo- 
eophical  and  scientific  ideas,  we  are  at  the  same  time  following 
the  laws  of  the  development  of  thought.  It  is  this  fact  which 
makes  the  history  of  philosophy  and  of  the  various  sciences  so 
instructive.  It  was  with  this  object  in  view,  to  take  but  a  single 
example,  that  Whewell  wrote  his  famous  History  of  the  Inductkie 
Sciences.  He  was  interested,  that  is,  not  so  much  in  the  mere  facts 
and  names  with  which  he  dealt,  as  in  showing  the  nature  of  thinking 
and  the  methods  which  had  been  employed  in  gaining  a  knowledge 
of  the  world.  This  is  made  very  clear  in  the  introduction  to  another 
work  of  Whewell  from  which  I  quote :  "  We  may  best  hope  to 
understand  the  nature  and  conditions  of  real  knowledge  by  studying 
the  nature  and  conditions  of  the  most  certain  knowledge  which  we 
possess  ;  and  we  are  most  likely  to  learn  the  best  methods  of  discov- 
ering truth  by  examining  how  truths,  now  universally  recognized, 
have  reallv  been  discovered.  Now  there  do  exist  among  us  doc- 
trines  of  solid  and  acknowledged  merit  certainly,  and  truths  of  which 
the  discovery  has  been  received  with  universal  applause.  These 
constitute  what  we  commonly  term  sciences ;  and  of  these  bodies  of 
exact  and  enduring  knowledge  we  have  within  our  reach  so  large  a 
collection  that  we  may  hope  to  examine  them  and  the  history  of 


■W!";^;^- 


i6 


THE  STANDPOINT  AND   PROBLEM   OF   LOGIC 


^. 


^■1 


v\ 


their  formation  with  a  good  prospect  of  deriving  from  the  study  such 
instruction  as  we  need  seek."^ 

We  have  been  insisting  that  the  materials  for  the 
study  of  logic  are  to  be  found  mainly  In  the  records 
which  we  possess  of  what  thinking  has  actually  accom- 
plished. Our  own  consciousness,  it  was  said,  can  supply 
but  a  very  small  quantity  of  material.  To  learn  what 
thinking  is,  one  must  have  as  broad  a  survey  as  possible 
of  its  achievements. 

But  there  is  another  side  to  the  matter.  It  must  never 
be  forgotten  that  it  is  the  actual  operations  of  thought 
with  which  logic  is  concerned.  The  words  and  proposi- 
tions which  express  the  results  of  thinking  must  never  be 
allowed  to  take  the  place  of  the  thoughts  themselves. 
Now,  we  cannot  directly  study  the  thoughts  of  any  other 
individual.  It  is  only  in  so  far  as  we  interpret,  through 
our  own  consciousness,  the  records  of  what  thinking  has 
done,  that  these  records  are  able  to  throw  any  light 
upon  the  problem  of  logic.  So  in  this  study,  as  else- 
where, we  must  find  the  key  to  the  material  in  our  own 
consciousness.  If  we  are  to  gain  any  real  ideas  of  the 
character  of  the  thinking  processes  by  means  of  which 
the  sciences  have  been  built  up,  we  must  reproduce 
these  in  our  own  minds.  One's  own  consciousness 
must  after  all  furnish  the  key  which  makes  intel- 
ligible the  account  of  the  various  steps  which  the 
thought  of  mankind  has  taken  in  building  up  science 
or  knowledge. 

1  Whewell,  History  of  Scientific  Ideas,  3d  ed.,  Vol.  I.,  p.  4. 


•^^. 


7   LOCIIC 


§4.    THE  MATERIAL  OF   LOGIC 


17 


111  the  study  such 

crials  for  the 
n  the  records 
:tually  accom- 
lid,  can  supply 
fo  learn  what 
ey  as  possible 

It  must  never 

ns  of  thought 

s  and  proposi- 

must  never  be 

;s  themselves. 

s  of  any  other 

Dret,  through 

thinking  has 

ow  any  light 

udy,  as  else- 

al  in  our  own 

ideas  of  the 

ans  of  which 

St  reproduce 

onsciousness 

makes   intel- 

5    which    the 

g  up  science 


References 

The   following    references    may   be   given   in   connection   with 
§§  I  and  2 : — 

C.  Sigwart,  Lo/^/c,  Vol.  I.,  General  Introduction. 
V.  II.  Bradley,  T/w  Pri)uiplcs  of  Loi^ic,  pp.  i-io. 
15.  Bosanquet,  Logic,  Vol.  I.,  Introduction. 

H.  L.  iMansel,  Proki^oinctia  Loi^ka,  Chap.  I. 
R.  Adamson,  The  first  part  of  the  article  '  Logic  '  in  the  Encyclo- 
pcrdia  Ih'itaiinica. 

D.  G.   Ritchie,  The  Relation  of  Logic  to  Psychology,  Philos. 
Rcviciv,  Vol.  v.,  pp.  585-600,  Vol.  VI.,  pp.  1-17. 


I.,  p.  4. 


i 


); 


>^ 


I 


>  -  i 


vt 


CHAITICR    II 

AN    HISTOKICAI.    SKETCH    OI'    r.OCIC 

§   5.    The   Logic   of   the   Greeks :    Aristotle.  —  In    the 

fourth  and  fifth  centuries  before  Christ,  a  great  interest 
in  debate  and  pubhc  controversy  spran^;  up  in  Athens. 
There  were  several  reasons  for  this.  In  the  first 
place,  the  Athenians  of  this  period  were  a  very  acute 
and  intellectual  people ;  they  therefore  required  some 
outlet  for  their  mental  activities.  The  va^-ious  sciences 
of  nature  which  occupy  so  much  of  the  thought  of  the 
modern  world  did  not  exist  at  that  time,  nor  did  the 
interest  exist  which  was  necessary  to  create  them.  For 
although  the  Greeks  had  the  greatest  love  and  rever- 
ence for  nature,  their  interest  in  natural  objects  was 
rathe*  like  that  of  the  poet  and  the  artist,  than  that  of 
the  modern  man  of  science ;  in  other  words,  they  were 
content  to  enjoy  the  beauty  of  natural  objects,  and  to 
take  delight  in  the  harmonies  of  sound  and  color  which 
their  senses  presented  to  them.  They  had  no  desire  to 
pull  things  to  pieces  to  see  how  they  are  made,  or  to 
discover  the  laws  according  to  which  they  act,  and  so 
their  mental  energy  and  mental  acuteness  found  its 
chief  outlet  in  argumentative  controversy,  and  public 
debating  became  one  of  their  favourite  diversions.  The 
Athenians  of  those  days  used  to  argue,  from  the  pure 
love  of  argument,  wherever  they  met,  —  in  the  market- 

i8 


^^^. 


§  5-    Tlll^   LOGIC  Ol    TIIK   GKKKKS 


19 


IC 

le.  —  In    the 

^rcat  interest 

ip  in  Athens. 

In    the    first 

a  very  acute 

:quired  some 

ions  sciences 

lOLight  of  the 

nor  did  the 

them.     For 

e  and  rever- 

objects  was 

than  that  of 

Is,  they  were 

jects,  and  to 

color  which 

no  desire  to 

made,  or  to 

act,  and  so 

s   found   its 

and   public 

sions.     The 

m  the  pure 

the  market- 


place, in  the  groves  and  gardens,  and  at  their  meals  and 
banquets. 

There  was  in  addition,  however,  a  very  practical 
reason  why  it  was  necessary  and  desirable  for  one  to 
be  able  to  argue  well.  A  man  of  })ro])erty  in  Athens 
was  constantly  exposed  to  lawsuits,  and  was  obliged  to 
be  his  own  lawyer  and  defend  his  cause  by  ])leading 
before  the  judges.  It  was  of  the  utmost  i)ractical 
importance,  then,  that  he  should  be  able  to  state  his 
cause  well,  and  should  be  master  of  all  the  arts  by 
which  the  judges  would  be  likely  to  be  influenced. 
Under  these  circumstances,  it  is  not  difficult  to  under- 
stand why  the  art  of  public  speaking  came  to  be 
regarded  in  Athens  as  a  necessary  part  of  education. 
And,  in  response  to  this  demand,  there  arose  a  class  of 
teachers  called  Sophists,  who  made  it  their  business  to 
instruct  young  men  in  all  the  practical  affairs  of  life, 
and  especially  in  the  art  of  public  speaking,  or  rhetoric, 
as  it  was  called.  The  Sophists  do  not  seem  to  have 
made  it  their  object  to  teach  truth  to  their  pupils,  or 
to  inculcate  in  them  a  love  and  reverence  for  truth ; 
they  rather  sought  to  make  those  whom  they  taught 
clever  men  of  the  world.  In  teaching  the  art  of  argu- 
mentation or  public  speaking  they  did  not  seek  to  point 
out  the  methods  by  which  true  conclusions  could  be 
reached,  but  rather  taught  the  arts  by  which  the  judges 
could  be  persuaded,  and  tricks  for  the  discomfiture  of 
one's  adversary.  The  rhetoric  of  the  Sophists,  in  other 
words,  was  not  a  science  of  reasoning,  but  an  art  of 
persuasion  and  of  controversy.  It  was  not  necessary 
to  have  any  real  knowledge  of  the  subject  under  dis- 


20 


AN    IIISIOKKAI,   SKI'iVII    ( )!•    I.OCIC 


I 


III 


I  ii 


cussioii  ill  order  to  argue  well,  but  only  to  be  well 
versed  in  all  the  arts  of  i)ersuasi()n,  and  (|uieU  to  take 
advantage  of  the  omissions  of  an  oi)i)onent. 

The  theory  on  whieh  the  teaching  of  the  Sophists 
was  based  is  usually  known  as  scepticism.  The 
Sophists,  that  is,  had  come  to  the  conclusion  that  it 
is  impossible  to  find  any  fixed  standard  of  truth. 
Looking  at  the  diversity  of  individual  opinions  and 
of  individual  feelings,  they  declared  that  knowledge 
or  truth  as  something  objective,  or  the  same  for  all, 
is  an  illusion.  Only  individual  opinions  exist;  there  is 
no  standard  by  reference  to  which  these  opinions  may 
be  measured.  It  is  impossible,  then,  to  distinguish 
false  opinions  from  true.  Indeed,  the  words  'truth' 
and  '  falsehood '  can  have  no  real  meaning ;  each  indi- 
vidual must  be  the  measure  of  truth  for  himself. 

Moreover,  in  the  oj)inion  of  the  Sophists,  the  same 
state  of  things  exists  with  regard  to  our  moral  ideas. 
There  is  no  standard  of  right  and  wrong,  just  as  there 
is  no  standard  of  trutli  and  falsehood.  Each  man 
has  the  right  to  choose  what  he  regards  as  most 
advantageous  for  himself.  The  traditional  rules  of  ^ 
morality  have  no  authority  over  the  individual,  nor  is 
it  possible  to  discover  any  rules  ot  morality  which  arc 
binding  on  all  men.  It  is  the  part  of  wisdom  to  con- 
sult one's  own  interest  in  acting,  and  to  seek  to  secure 
one's  own  advantage.  Moral  distinctions,  like  logical 
distinctions,  are  purely  relative  and  individual. 

Socrates  was  the  great  opponent  of  the  ethical  scepti- 
cism of  the  Sophists.  They  had  concluded,  from  the 
diversity  of  individual  opinion  on  moral  questions,  that 


I 


-V  ^  V.     H 


c 

to  1)C  wcl) 
lick  lo  take 
t. 

ic   Sopln'sts 

:isiii.       The 

sion  tliat  it 

of    truth. 

linions    and 

knowlcd^^c 

iiic   for  all, 

st ;  there  is 

inions  may 

distinguish 

rds  'truth' 

each  indi- 

mself. 

the  same 
oral   ideas, 
as  there 
ach    man 
as    most 
rules   of  ^ 
al,  nor  is 
which  are 
m  to  con- 
to  secure 
c  logical 
d. 

:alscepti- 
from  the 
ions,  that 


§5.    TIIF   T.or.TC  OF  TIIK  (IKKKKS 


31 


I 


?>^ 


there  is  no  real  or  absolute  distinction  between  right  and 
wrong.  Socrates,  however,  was  convinced  that,  if  one  e.\. 
amined  more  carefully  the  nature  of  the  judgments  which 
men  |)ass  on  matters  of  right  and  wrong,  one  would  fuul 
common  elements  or  ideas.  It  is  possible,  he  believed, 
to  fuul  a  fixed  standard,  both  in  matters  of  theory  and  in 
matters  of  practice.  This  common  element,  however, 
is  not  to  be  discovered  in  sensation,  nor  in  feelings  of 
pleasure  and  pain ;  these  are  purely  individual,  and 
can  never  .serve  as  a  universal  standard,  liut  beneath 
the  diversity  of  sensation  and  feelings  there  is  the 
thought,  or  concept,  which  is  common  to  all  men. 
When  rational  beings  come  to  understand  each  other, 
they  must  agree  as  to  the  nature  of  the  fundamental 
virtues, — justice,  temperance,  courage,  etc.  It  is  true 
that  few  men  have  thought  about  these  matters,  and 
are  able  to  express  their  meaning  clearly ;  but  every 
man,  as  a  rational  being,  carries  these  fundamental 
notions  in  his  mind.  Now,  in  order  to  refute  the 
moral  scepticism  of  the  Sophists  (and  it  was  this  side 
of  their  teaching  which  Socrates  especially  opposed), 
it  is  necessary  that  the  ethical  notions,  or  concepts, 
which  are  implicit  in  the  minds  of  men  shall  be  drawn 
out  and  carefully  defined.  How  is  this  to  be  accom- 
plished ?  Socrates  did  not  undertake  to  teach  men 
what  ideas  they  should  hold  regarding  the  nature  of 
any  of  the  virtues ;  he  rather  made  them  pai  tncrs 
in  an  investigation,  and  by  means  of  skilful  questions 
tried  to  assist  them  in  discovering  the  real  nature  of 
goodness  for  themselves.  Another  point  to  be  noticed 
is  rhat  the  definition  of  the  various  virtues  was  reached 


>jy'ifi»   'm-f^  —  ■ 


22 


AN    HISTORICAL   SKETCH    OF   LOGIC 


I 


% 


'  ! 


as  a  result  of  comparing  the  views  of  a  number  of 
individuals.  In  this  way,  by  comparing  the  opinions 
of  many  men,  of  different  professions,  and  of  different 
grades  of  society,  he  was  able  to  separate  what  was 
merely  individual  and  relative  in  these  opinions,  from 
what  was  unchanging  and  absolute. 

Plato,  the  disciple  of  Socrates,  continued  the  work 
of  his  master.  He  did  not  confine  his  attention  wholly 
to  the  moral  conceptions,  but  showed  that  the  Socratic 
method  could  also  be  used  to  refute  the  intellectual  scep- 
ticism of  the  Sophists.  In  other  words,  he  proved  that 
in  'he  concept,  or  thought,  as  opposed  to  sensation,  a 
standard  of  truth  is  to  be  found,  as  well  as  a  standard 
of  morality.  Knowledge  arises  from  thinking,  and  it 
is  possible  to  compare  our  thoughts,  however  impossi- 
ble it  may  be  to  find  any  basis  of  comparison  in  our 
sensations. 

Plato's  disciple,  Aristotle,  is  of  great  importance  in 
the  history  of  logic.  He  undertook  a  thorough  investi- 
gation of  the  process  of  reasoning,  and  sought  to  show 
what  conditions  and  principles  are  necessarily  involved 
in  reaching  certainty.  Aristotle  was  thus  the  founder  of 
logic,  as  well  as  of  psychology,  zoology,  and  a  number 
of  other  sciences.  His  most  important  logical  works 
are  the  Categories,  De  Interprctatio)ic,  Prior  Analytics, 
Posterior  Analytics,  Topics,  and  the  Sophistical  Elenchiis, 
a  treatise  on  Fallaf^ies.  These  writings  came  after- 
wards to  be  known  as  the  Organon  (or  scientific  instru- 
ment) of  Aristotle.  They  contained,  in  the  first  place, 
what  we  call  theory  of  knowledge  (a  discussion  of  the 
structure  of  knowledge,  and  of  the  scientific  principles 


n 


§  5.     THE   LOGIC  OF  TliK   GREEKS 


23 


number  of 
le  opinions 
jf  different 
;  what  was 
iiions,  from 

d  the  work 
ition  wholly 
he  Socratic 
ectual  scep- 
proved  that 
sensation,  a 
a  standard 
cing,  and  it 
/er  impossi- 
ison  in  our 

Dortance  in 
Li<xh  investi- 
it  to  show 
y  involved 
founder  of 
a  number 
ical  works 
Analytics, 
I  E/ciichus, 
ame   after- 
ific  instru- 
rst  place, 
ion  of  the 
principles 


upon  which  it  rests),  which  formed  an  essential  part  of 
Aristotle's  philosophical  system.  But  they  also  fur- 
nished the  practical  application  of  these  principles.  In 
his  doctrine  of  the  syllogism,  which  is  found  mainly  in 
the  Prior  Analytics,  he  showed  what  are  the  only  valid 
forms  of  reasoning,  and  thus  furnished  the  pattern  or 
type  to  which  all  proofs  must  conform.  He  also  classi- 
fied, in  his  work  on  Fallacies,  the  various  species  of 
false  reasoning ;  and  showed  how  false  arguments  could 
be  refuted  and  exposed  by  the  principles  which  he  had 
discovered.  The  form  to  which  Aristotle  maintained  that 
all  true  reasoning  can  be  reduced  was  as  follows  :  — 

All  men  are  mortal, 
Socrates  is  a  man, 
Therefore  Socrates  is  mortal. 

This  is  called  a  Syllogism,  and  it  is  made  up  of  three 
propositions.  The  first  two  propositions  are  called 
Premises,  and  the  last  the  Conclusion.  Every  piece  of 
reasoning,  all  proof,  can  be  reduced  to  this  form.  Of 
course,  the  propositions  which  make  up  the  syllogism 
do  not  always  stand  in  this  order,  and  sometimes  one  of 
them  may  be  omitted.  Thus  in  the  argument :  '  he 
ought  to  be  supported  by  the  state,  for  he  is  an  old 
soldier,'  the  conclusion  stands  first,  and  one  premise  is 
wanting  entirely.  It  is  easy  to  see,  however,  that  the 
real  argument  when  properly  arranged  is  equivalent  to 
this :  — 

All  old  soldiers  ought  to  be  supported  by  the  state, 

He  is  an  old  soldier, 

Therefore  he  ought  to  be  supported  by  the  state. 

Now  the  part  of   Aristotle's  logic   which   was   best 


I 


24 


AN    HISTORICAL   SKEi'CH   OF   LOGIC 


'l 


; 


« 


\  i* 


worked  out,  was  a  theory  of  proof  or  demonstration  by 
means  of  the  syllogism.  Here  he  showed  clearly  the 
various  ways  in  which  different  kinds  of  propositions 
could  be  combined  as  premises  to  yield  valid  conclu- 
sions, and  proved'  that  no  conclusion  could  be  drawn 
from  other  combinations.  This  part  of  the  Aristotelian 
logic  has  come  down  to  us  almost  unchanged,  and  is 
the  subject  of  Part  I.  of  the  present  volume. 

It  will  be  noticed  that,  in  the  doctrine  of  the  syllogism, 
Aristotle  was  dealing  with  that  kind  of  reasoning  which 
undertakes  to  demonstrate  the  truth  of  some  fact, 
by  showing  its  relation  to  a  general  principle  which 
every  one  admits.  In  other  words,  this  part  of  his 
work  may  be  called  the  logic  of  proof  or  demonstra- 
tion. Aristotle  was  at  one  time  of  his  life  a  teacher  of 
rhetoric,  and  he  seemed  always  to  have  aimed  at  putting 
this  art  of  reasoning  on  a  scientific  basis.  That  is,  for 
the  rules  of  thumb  and  questionable  artific^.s  of  the 
Sophists,  he  wished  to  substitute  general  laws  and 
methods  of  procedure  which  were  based  upoi.  a  study 
of  the  principles  and  operations  of  reason.  By  com- 
plying with  the  rules  which  he  laid  down,  an  argument 
will  necessarily  gain  the  assent  of  every  rational  being. 

But  we  do  not  employ  our  reason  merely  in  order  to 
demonstrate  to  ourselves  or  to  others  what  we  already 
know.  We  seek  to  discover  new  facts  and  truths  by 
its  aid.  In  other  words,  we  not  only  wish  to  prove  what 
is  already  known,  but  also  to  discover  new  facts,  and  we 
need  a  logic  of  Discovery,  as  well  as  a  logic  of  Proof. 
This  distinction  between  proof  and  discovery  corre- 
sponds in  general  to  that  between  Deduction  and  In- 


A 


^x. 


ion  by 
rly  the 
)sitions 
conclu- 

drawn 
totelian 

and  is 

Uogism, 
cr  which 
lie   fact, 
e   which 
:   of   his 
monstra- 
;acher  of 
putting 
lat  is,  for 
of  the 
\vs   and 
a  study 
y  com- 
rsfument 
1  being, 
order  to 
already 
uths  by 
ve  what 
,  and  we 
f  Proof, 
corre- 
and  In- 


J 


§  5.    THE   LOGIC  OF  THE   GREEKS 


25 


duction.  Deduction  is  the  process  of  showing  how 
particular  facts  follow  from  some  general  principle  which 
everybody  admits,  while  Induction  shows  the  methods 
by  which  general  laws  are  obtained  from  an  observation 
of  particular  facts.  Now  Aristotle,  as  we  have  seen, 
furnished  a  very  complete  theory  of  Deduction,  or 
method  of  proof.  But  he  did  not  treat  of  Induction, 
or  the  method  of  passing  from  particular  facts  to  gen- 
eral laws,  with  anything  like  the  same  completeness. 
Moreover,  what  he  did  write  on  this  subject  received  no 
attfintion  for  mar  /  centuries.  Aristotle  was  himself  a 
great,  scientific  observer,  and  may  wC^  be  regarded  as 
the  father  of  the  natural  history  sciences.  But,  in  his 
logical  writings,  his  main  object  seems  to  have  been  to 
present  a  true  theory  of  argumentation,  as  opposed  to 
the  false  theories  of  the  Sophists.  Science,  too,  was 
only  in  its  beginning  when  Aristotle  wrote,  and  it  was 
impossible  for  him  to  foretell  the  method.s  of  discovery 
which  it  has  actually  employed. 

After  Aristotle's  death  (322  r.c),  and  after  the  loss 
of  Athenian  independence,  there  was  a  great  decline  of 
interest  in  matters  of  mere  theory  which  had  no  direct 
application  to  the  practical  affairs  of  life.  The  Stoic 
school  did  make  some  slight  additions  to  logical  theory, 
but  like  their  opponents,  the  Epicureans,  they  regarded 
practice,  tiie  art  of  living  well,  as  the  supreme  wisdom 
of  life.  The  Romans,  who  derived  their  knowledge  of 
Greek  philosophy  largely  from  the  Stoics,  were  also  in- 
terested in  the  practical  advantages  of  logic,  rather  than 
in  its  theoretical  side.  It  was  the  possibilit._y  01  aj^ply- 
ing  the  laws  of  logic  to  rhetoric  and  public  speaking 


t  ^' 


/ 


26 


AN   HISTORICAL   SKKTCII   OF   LOGIC 


\ 


I 

i.- 


^V 


>        y 


which  especially  interested  Cicero,  who  was  the  first  to 
make  Latin  paraphrases  and  adaptations  of  Greek  logic 
in  his  rhetorical  works. 

§  6.  Logic  during  the  Middle  Ages.  —  For  more  than 
seven  hundred  years,  during  the  Middle  Ages,  the  Greek 
language  and  literature  was  almost  unknown  in  Western 
Europe.  During  this  time,  almost  the  only  sources  of 
information  regarding  logic  were  Latin  translations  of 
Aristotle's  Categories,  and  of  an  Introduction  to  the  same 
work  by  Porphyry,  who  lived  232-303  a.d  Both  of  these 
translations  were  made  by  Boethius (470-525),  who  is  best 
known  as  the  author  of  T/ie  Consolations  of  Philosopliy. 
Even  when  scholars  again  became  acquainted  with  the 
original  works  of  Aristotle,  in  the  latter  part  of  the 
Middle  Ages,  they  did  not  really  understand  their  true 
significance.  They  took  the  husk,  one  may  say,  and 
neglected  the  kernel.  They  adopted  the  Aristotelian 
logic  as  an  external  and  arbitrary  set  of  rules  for  the 
guidance  of  thinking,  and  neglected  entirely  the  sci- 
entific theory  upon  which  these  rules  were  based.  A 
great  deal  of  ingenuity  was  also  shown  in  subdividing 
and  analyzing  all  possible  kinds  of  argument,  and  giv- 
ing the  particular  rule  for  each  case.  This  process  of 
making  distinctions  was  carried  so  far  that  scholastic 
logic  became  extremely  cumbersome  and  artificial.  Its 
pretensions,  however,  rapidly  increased ;  it  claimed  to 
furnish  a  complete  instrument  of  knowledge,  and  a  sure 
standard  for  discriminating  betw^en  truth  and  false- 
hood. 

It  is  not  very  difficult  to  understand  why  this  set  of  logical  rules 


Hi 


"■»-      V 


^»^ — 4- 


§  6.     LOGIC   DURIXG  THE  MIDDLE   AGES 


27 


glV- 

Iss  of 

lastic 

Its 

ja  to 

sure 

ialse- 

rules 


seemed  so  satisfactory  to  tlic  age  of  Scholasticism.  The  men  of  this 
period  liad  no  desire  to  increase  tlieir  knowledge  ;  they  supposed 
that  they  were  already  in  possession  of  everything  which  was  worth 
knowing.  Their  only  object  was  to  weave  this  kntnvledge  into  a 
system,  to  show  the  connection  and  interdependence  of  all  its  parts, 
and  thus  to  put  it  beyond  the  possibility  of  attack.  And  for  this 
purpose,  the  school  logic  was  admirably  adapted  ;  it  was  always 
possible  to  bring  every  case  which  could  arise  under  one  or  other  of 
its  rules. 

There  is  no  doubt  that  the  Aristotelian  logic  had 
a  real  value  of  its  own,  and  that  it  exercised  a  very 
important  influence  upon  Western  civilization,  even  in 
the  form  in  which  it  was  taught  by  the  Schoolmen ; 
but  there  is,  of  course,  nothing  complete  or  final  about 
it.  Its  main  purpose,  as  we  have  already  seen,  was  to 
furnish  a  method  by  means  of  which  the  knowledge  we 
already  possess  may  be  so  arranged  as  to  be  absolutely 
convincing.  But  the  centre  of  intellectual  interest  has 
changed  since  medireval  times.  We  are  not  content 
merely  to  exhibit  the  certainty  and  demonstrative  char- 
acter of  the  knowledge  which  we  already  have,  but  we 
feel  that  there  is  a  great  deal  of  importance  still  to  be 
discovered.  So  that,  in  modern  times,  one  may  say  the 
desire  to  make  discoveries,  and  so  add  to  the  general 
stock  of  knowledge;  has  taken  the  place  of  the  medi- 
ceval  ideal  of  showing  that  the  traditional  doctrines 
taught  by  the  church  are  absolutely  certain  and  con- 
vincing. And  when  men  became  conscious  of  the 
importance  of  gaining  new  knowledge,  and  especially 
knowledge  about  nature,  they  at  once  saw  the  neces- 
sity for  a  new  logic,  or  doctrine  of  method,  to  aid  them 
in  the  undertaking. 


./ 


28 


AN    ITISTORK^M,   SKETCH   OF   T.OCUC 


I 


^     J 

f 


VL-l. 


1 


§  7.  The  Logic  of  Bacon.  —  All  the  c^reat  thinkers 
of  the  sixteenth  and  seventeenth  centuries  saw  clearly 
that  the  school  logic  is  simply  a  method  of  showing  the 
certainty  of  the  knowledge  we  already  possess,  and 
does  not  aid  us  at  all  in  making  new  discoveries.  A 
new  method,  they  all  declared,  was  an  absolute  neces- 
sity. The  new  point  of  view  was  put  most  clearly  and 
eloquently  by  the  famous  .Francis  Bacon  (1561-1026), 
at  one  time  Lord  Chancellor  of  England.  Bacon  called 
his  work  on  logic  the  Novum  Orgamtui,  thus  contrast- 
ing it  with  the  Organon^  or  logical  treatises  of  Aristotle. 
An  alternative  title  of  the  work  is,  True  Siiggcstions  for 
the  Interpretation  of  Nature.  ]^acon  begins  this  work 
by  showing  the  advantages  to  be  gained  from  a  know- 
ledge of  nature.  It  is  man's  true  business,  he  tells  us, 
to  be  the  minister  and  interpreter  of  nature,  for  it  is  only 
by  becoming  acquainted  with  the  laws  of  nature  that  we 
are  ever  able  to  take  advantage  of  them  for  our  own 
ends.  "Knowledge  and  human  power  are  synonymous, 
since  ignorance  of  the  cause  prevents  us  from  taking 
advantage  of  the  effect."  The  discovery  of  the  laws  of 
nature,  which  is  therefore  of  so  great  practical  impor- 
tance, cannot  be  left  to  chance,  but  must  be  guided  by 
a  scientific  method.  And  it  is  such  a  method  which 
Bacon  endeavours  to  supply  in  the  Novum  Organum. 

The  method  which  Bacon  proposed  seems  to  us  very 
simple.  If  we  would  gain  new  knowledge  regarding 
nature,  he  says,  and  regarding  natural  laws,  we  must 
go  to  nature  herself  and  observe  her  ways  of  acting. 
Facts  about  nature  cannot  be  discovered  from  logical 
propositions,  or  from  syllogisms ;  if  we  would  know  the 


§  S.     LOGIC   SINCE  THE   TIME   OF   BACON 


29 


ing 
of 
)r- 

>y 


law  of  any  class  of  phenomena,  we  must  observe  the  par- 
ticular facts  carefully  and  systematically.  It  will  often 
.)e  necessary,  also,  to  put  pointed  questions  to  niiture 
by  such  experiments  as  will  force  her  to  fjjive  us  the 
information  we  want.  Knowledge,  then,  must  begin 
with  observation  of  particular  facts;  and  only  after  we 
have  made  a  great  number  of  particular  observations, 
and  have  carefully  classified  and  arranged  them,  taking 
account  of  all  the  negative  cases,  are  we  able  to  discover 
in  thenvthe  general  law.  No  hypotheses  or  guesses  are 
to  be  made  ;  but  we  must  wait  until  the  tabulations  of 
the  particular  phenomena  reveal  the  general  '  form  '  or 
principle  which  belong  to  them  all. 

It  will  be  frequently  necessary  to  refer  to  Bacon's 
work  in  what  follows.  At  present,  it  is  sufficient  to 
note  that  Bacon  showed  that  a  knowledge  of  nature 
cannot  be  attained  through  general  ropositions  and 
logical  arguments,  but  that  it  is  necessary  to  begin 
with  the  observation  of  particular  facts.  H^-  .  "ipha- 
sized,  also,  the  importance  of  systematic  observation 
and  carefully  planned  experiments,  and  showed  that 
knowledge  must  begin  with  facts  of  perception.  This 
is  the  method  of  ^induction,  and  Bacon  is  usually  said 
to  have  been  the  founder  of  the  inductive  sciences  of 
nature. 


§  8.  Logic  since  the  Time  of  Bacon.  —  Another  and 
quite  different  method  of  extending  knowledge  was  pro- 
posed by  the  great  Frenchman,  Descartes  (i  596-1650), 
who  took  mathematics  as  the  type  to  which  all  know- 
ledge should  conform.     That  is,  he  supposed  that  the 


30 


AN    HISTORICAL   SKHTCII    ()!•    LOGIC 


true  method  of  cxtcndincj  knowledge  was  to  begin  with 
general  principles,  whose  truth  could  not  be  doubted, 
and  to  reason  from  them  to  the  necessary  character 
of  particular  facts.  Descartes  and  his  followers  thought 
that  it  was  possible  to  discover  certain  axiomatic  propo- 
sitions from  which  all  truth  could  be  derived  through 
reason.  They  thus  emphasized  Deduction  rather  than 
Induction,  and  reasoning  rather  than  observation  and 
experiment.  The  spirit  of  Bacon's  teaching  was,  how- 
ever, continued  in  England  by  John  Locke,  in  the 
Essay  Conccruing  Human  Understanding  (1690).  Dur- 
ing the  next  centuries,  philosophical  thinkers  were 
divided  into  two  great  schools,  —  Rationalists,  or  those  '^ 
who  agreed  in  the  main  with  Descartes,  and  Empiricists, 
or  Sensationalists,  who  followed  the  teachings  of  Bacon 
and  Locke. 

Although  the  natural  sciences  made  great  advances 
during  the  seventeenth  and  eighteenth  centuries,  there 
seems  to  have  been  no  effort  made  to  analyze  and 
describe  the  methods  which  were  actually  being  em- 
ployed. In  England,  at  least,  it  seems  to  have  been 
assumed  that  all  discoveries  were  made  by  the  use  of 
the  rules  and  methods  of  Bacon.  One  of  the  first 
writers  to  attempt  to  explain  the  method  used  by  the 
natural  sciences  was  Sir  John  Hcrschel  (i 792-1 871). 
His  work.  Discourse  on  the  Study  of  Natural  P/iilosop/iy, 
was  published  in  1832.  A  little  later,  and  with  the 
same  object  in  view^,  William  Whewell  (i 794-1 866), 
afterwards  Master  of  Trinity  College,  Cambridge,  un- 
dertook his  History  of  the  Inductive  Sciences,  which 
was  followed  some  time  after  by  the  Philosophy  of  the 


§8.     LOGIC   SINCi:   TIIL:  time   ok   lUCON 


31 


in  with 
oubtcd, 
raracter 
thought 
;  propo- 
through 
ler  than 
tion  and 
^as,  how- 
j,  m  the 
)).     Dur- 
ers   were 
,  or  those 
nphicists, 
of  Bacon 

advances 
ries,  there 
ilyze   and 
bcuig  em- 
lave  been 
[he  use  of 
the  first 
led  by  the 
I92-1871). 
yhilosophyy 
with  the 
794-1866), 
)ridge,  un- 
\ccs,  which 
\phy  of  the 


liidiict'r,'  Sciences.  The  man,  however,  who  did  most 
towards  putting  the  study  of  logic  on  a  new  basis  was 
John  Stuart  iMiil  (1806-1873),  the  first  edition  of  whose 
L(\i^ric  appeared  in  1843.  We  shall  have  frequent  occa- 
sion to  refer  to  this  work  in  future  discussions.  It  is 
sufficient  to  say  here  that  Mill  continues  the  empirical 
tradition  of  the  earlier  English  writers  in  his  general 
philosophical  position.  Mill's  book  gave  a  great  im- 
pulse to  the  study  of  logic.  13efore  it  was  published, 
writers  on  the  subject  had  confined  their  attention 
almost  exclusively  to  the  syllogistic  or  deductive  rea- 
soning. Mill,  however,  emphasized  strongly  the  impor- 
tance of  induction  ;  indeed,  he  regarded  induction  as 
the  only  means  of  arriving  at  new  truth,  deduction 
being  merely  a  means  of  systematizing  and  arranging 
what  we  already  know.  Though  few  logicians  of  the 
present  day  adopt  this  extreme  view,  the  importance  of 
inductive  methods  of  reasoning,  and  the  necessity  of 
studying  them,  have  now  become  generally  recognized. 
Most  modern  writers  on  logic  devote  a  considerable 
amount  of  attention  to  induction.  The  reader  will  find 
that  Part  II.  of  the  present  volume  deals  with  this 
subject. 

There  is  still  another  side  of  logic  which  has  been 
developed  in  the  English-speaking  world  since  the  time 
of  Mill,  though  it  is  a  direct  continuation  of  the  move- 
ment started  in  German/  by  Kant  1  .ure  than  a  hun- 
dred years  ago.  The  so:alled  'modern'  logic  has  laid 
aside  the  formalism  and  paradoxical  mode  of  expression 
adopted  by  Hegel,  but  the  fundamental  conceptions 
with  which  it  works  are  essentially  the  same  as  those 


32 


AN   IIISTOUKJAL   SKKTCII   OK   I,(){JIC 


)i 


employed  by  the  latter  in  his  Ulsscnsc/iaft  thr  Logik 
( i8ir)-i,Si<S).  It  has  been  witliin  the  last  twenty  years 
that  the  results  of  (lerman  idealism  —  the  doctrines  of 
Kant,  Fichte,  Schelling,  and  llegel  —  have  become 
naturalized  in  l^ngland  and  America.  And  largely  as 
a  consequence  of  these  teachings,  a  new  conception  of 
the  nature  of  thought  has  grown  up,  and  given  rise  to 
investigations  which  may  be  said  to  have  created  a 
'  modern '  logic  that  is  fairly  entitled  to  rank  beside 
its  sister  science,  the  *  new '  psychology. 

The  Aristotelian  doctrine  of  the  syllogism  is  a  purely 
formal  science.  In  the  form  in  which  it  is  represented 
in  ordinary  text-books,  it  might  perhaps  be  more  prop- 
erly described  as  the  art  of  arranging  our  knowledge 
in  such  a  way  as  to  compel  assent.  The  'matter'  with 
which  thought  is  supposed  to  work  is  supplied  to  it  in 
form  of  concepts  and  judgments.  The  ])roblem  which 
formal  logic  has  to  solve  is  to  define  and  classify  the 
various  kinds  of  concepts  with  which  thought  operates, 
and  to  determine  the  various  relations  in  which  these 
stand  when  combined  into  judgments.  Similarly,  it 
has  to  show  what  combinations  of  judgments  can  be 
employed  as  premises  leading  to  valid  conclusions  in 
the  .syllogism.  The  criterion  of  truth  employed  in  these 
investigations  is  the  principle  of  non-contradiction  or 
consistency.  Inconsistent  combinations  of  concepts, 
that  is,  are  ruled  out ;  but  so  far  as  the  doctrine  of 
the  syllogism  goes,  anything  is  true  which  is  not  self- 
contradictory. 

Now,  without  questioning  the  practical  value  of  its 
canons,  it  is  obvious  that  formal  or  syllogistic  logic  does 


;ic 


§8.     L(.J(J1C   SINCE  THE  TIME  oE   IJACON 


33 


ift  (hr  Logik 
twenty  years 
i  doctrines  of 
have  become 
.ncl  largely  as 
conception  of 
given  rise  to 
Lve  created  a 
'  rank  beside 

5m  is  a  purely 
s  represented 
>e  more  prop- 
iir  knowledge 
*  matter '  with 
pplied  to  it  in 
roblem  which 
1  classify  the 
ght  operates, 
which  these 
Similarly,   it 
bents  can  be 
)nclusions  in 
loyed  in  these 
Itradiction  or 
|of   concepts, 
doctrine  of 
is  not  self- 
value  of  its 
lie  locric  does 


.not  take  any  account  of  many  of  ii  processes  of  every- 
day thought,  and  that  its  rules  go  but  a  little  way  in 
helping  us  to  dislinguisli  the  Mue  Irom  tiic  false.  I'or, 
in  the  first  place,  to  think  is  not  merely  to  combine  and 
arrange  ideas  already  in  our  possession.  This  might 
^o^enable  us  to  render  clearer  and  more  definite  what  we 
'•already  know,  but  would  never  enable  us  to  gam  new 
knowledge.  The  real  movement  of  thought  —  as  op- 
posed to  its  merely  iormal  procedure  —  consists  in  the 
formation  of  new  ideas  and  new  knowledge  through 
^actual  contact  with  the  world  of  experience.  A  com- 
plete account  of  the  intellectual  process,  then,  nuist 
deal  with  the  relation  of  the  mind  to  objects;  it  must 
investigate  the  various  activities  by  means  of  which 
thought  interprets  the  world  and  builds  up  the  various 
sciences  of  nature  and  of  man. 

The  recognition  of  the  importance  of  induction,  and 
pjOf  the  necessity  of  studying  the  methods  of  the  induc- 
tive  sciences   which   was   brought  about   by  Whewell, 
Mill,  and  others,  was  a  step  in  the  right  direction,  for 
Mt  called  attention  to  a  kind  of  thinking  which  occupies 
Ja  large  place  in  our  intellectual  life,  and  also  gave  rise 
,^0  a  truer  conception  of  the  nature  of  thought  itself, 
lut   even    IMill  did  not  reach   the   idea  which   guides 
odern  logicians,  that  thought  or  intelligence   is   one 
rom   beginning  to  end,  and   that   the  various  logical 
•|processes  are  all  parts  of  one  whole,  or  rather  ways  in 
rW'hich  intelligence  operates  in  different  circunistances, 
^or  at   different    stages   of   its    development.      He   still 
preats  of  logical  processes,  like  conception,  judgment, 
^nd   reasoning,  as  if   they  were   quite   separate   from 

D 


34 


AN    HISTORICAL  SKl/rciI   OF   LOC.IC 


each  other;  aiul,  as  has  ah'eady  been  noticed,  in  liis 
zeal  for  induction,  he  fails  completely  to  do  justice  to 
deductive  reasoning. 

As  opposed  to  the  division  of  mind  into  separate 
faculties,  the  thought  by  which  modern  logic  is  domi- 
nated is  that  of  the  unity  and  continuity  of  all  intel- 
lectual life.  Thought  is  regarded  as  an  organic,  living 
function  or  activity,  which  remains  identical  with  itself 
throughout  all  its  developing  forms  and  phases.  The 
problem,  accordingly,  which  logic  must  set  before  itself 
is  to  show  the  unity  and  interrelation  of  all  of  the 
intellectual  processes.  No  one  of  the  steps  or  stages 
in  this  process  can  be  completely  understood  when 
viewed  by  itself :  each  is  what  it  is  only  in  and  through 
its  connection  with  the  whole  of  which  it  forms  a  part. 
No  hard  and  fast  boundary  lines  arc  to  be  drawn  be- 
tween the  different  stages  of  the  reasoning  process,  but 
it  must  be  shown  that  the  whole  nature  of  intelligence 
is  involved  more  or  less  explicitly  at  each  step.  So 
far  only  the  broad  outlines  of  this  theory  have  been 
filled  in ;  but  the  conception  of  an  organism  whose 
parts  are  developing  in  mutual  relation  and  inter- 
dependence, promises  to  be  as  fruitful  when  applied 
to  logic  as  it  has  already  shown  itself  to  be  in  the 
other  sciences. 


1     '-' 


Besides  the  ordinary  histories  of  philosophy  the  reader  may  con- 
sult for  the  history  of  logic  :  Prantl,  Geschichte  der  Logik  iin  Abeiid- 
lande,  4  vols.,  Leipsic,  1855-1870;  which  extends,  however,  only  to 
the  close  of  the  medineval  period.  Harms,  Geschichte  der  Logik, 
Berlin,  1S81.  Ueberweg,  System  der  Logik,  4th  ed.,  1874;  E^,l,^ 
trans,  of  3d  ed.,  London,  1874.     Adamson,  article  'Logic,'  in  the 


\    > 


ilC 


§  S.     \.(H'.\r   SIN(  K    IIll",    IIMK  (»!■    HACON 


35 


oticcd,  in  his 
cU)  justice  to 

into  separate 
l()y;ic  is  clomi- 
y  of  all  intcl- 
or^^anic,  living 
cal  with  itself 

phases.     The 
et  before  itself 

of  all  of  the 
;teps  or  stages 
derstood  when 
in  and  through 
it  forms  a  part. 
3  be  drawn  be- 
ng  process,  but 

of  intelligence 

ach  step.  So 
jiory  have  been 
rganism    whose 

;ion  and  inter- 
when  applied 
If   to  be  in  the 


Kncvl.  Mrit..  ^tli   cd.     Sir  William    1  laniilloii's  Lcitutes  on  Logic^ 
also  contaiiiiii;,'  much  historical  informalion. 

Amoii;^  modern  works  on  lo^dc.  the  followin;^  may  he  nicntiont'd : 
J.  .S.  Mill,  A  System  of  Li\i:;k\  London,  ist  ed..  1843;  9th  iil..  1.S75. 
W.  .S.  Jcvon.s,  The  I'rincipics  ^y' .SV/W/tt-,  London.  1874;  2d  cd., 
i<S77.  Also,  by  the  same  author.  Studies  in  Dcduitivc  /.o_i:;ic,  1880; 
■M\i\  Pure  /.(\iiii\  1890.  \\.  Lotze,  Loi^ilc,  1874;  En<f.  trans..  Lon- 
don. 1 88 1  and  1888.  W.  Wundt,  Lo^iii/:,  2d  ed..  1896.  C.  Si>,'\vart, 
L<%'i/c,  2d  ed.,  1889 -1893;  En*;,  tran.s.,  London  and  New  York,  1895. 
The  newer  development  of  lo^ic  is  well  represented  hy  F.  IL  Hrad- 
'\Q)\T/te  Principles  of  Loi^ic,  London,  1886.  15.  Hosanciuet.  J^o^^ic, 
or  the  Moypholoi^y  of  Kmnvle(ii:;e,  London.  1888;  and  Ihe  /'Essentials 
of  Loj^ic,  London  and  New  York,  1895.  L.  T.  Hohhouse,  The  Theory 
of  h'no'-ii'ledi^e,  London.  1896.  may  also  be  mentioned  in  the  same 
group  of  writers,  althou<j;h  he  has  been,  perhaps,  more  inHuenced  by 
Mill  than  by  any  other  writer. 

■      The  following  works,  among  others,  have  proved  useful  as  text- 
^books :  W.  S.  Jevons,  Elementary  Lessons  in  I.Oi^ic,  London  and 
ew  York,  1870.     A.  IJain,  Lo^^^ir,  Deductive  and  Induct ive^  New 
ork.  1883.     J.  H.  Hyslop.  The  lUemcnts  of  Logic,  New  York,  1892. 
i^t/.  Minto,  Lof^^ic  Inductive  and  Deductive,,  New  York,  1894.      J.  G. 
ben,  Inductive  Logic,  New  York,  1896. 


he  reader  may  con- 
\>-  Logik  im  Abend- 
]s,  however,  only  to 
Vchichte  der  Logik, 
li  ed.,  1874;  Eng. 
Icle  'Logic,'  in  the 


.MJ 


f\ 


i 


PART    I.  — THE   SYLLOGISM 


CHAPTER    III 


THE  SYLLOGISM  AND  ITS  PARTS 


III 


\ 


■\     I 


§  9.  The  Nature  of  the  Syllogism.  —  The  theory  of 
the  syllogism,  as  has  been  already  stated  (§  5),  was 
first  worked  out  by  Aristotle.  And  it  stands  to-day 
in  almost  the  same  form  in  which  he  left  it.  A  few 
additions  have  been  made  at  different  points,  but  these 
do  not  affect  materially  the  main  doctrine.  In  deal- 
ing wdth  the  nature  of  the  syllogism,  we  shall  first 
try  to  understand  its  general  aim  and  purpose,  or  the 
results  which  it  seeks  to  bring  about.  We  shall  then 
have  to  analyze  it  into  the  parts  of  which  it  is  com- 
posed, and  to  examine  and  classify  the  nature  of  these 
elements.  Finally,  it  will  be  necessary  to  discover 
what  rules  must  be  observed  in  order  to  obtain  valid 
conclivsions,  and  to  point  out  the  conditions  which 
most  commonly  give  rise  to  error  or  fallacy. 

In  the  first  place,  it  is  to  be  noticed  that  syllogistic 
logic  deals  with  the  results  of  thinking,  rather  than 
with  the  nature  of  the  thought-process.  Its  object  is 
not  to  give  an  account  of  the  way  in  which  thinkinij; 
goes  on,  but  to  show  how  the  ideas  and  thoughts  which 
we  already  possess  may  be  combined  so  as  to  compel 

36 


§  9-     THE  NATURE  OF  THE  SYLLOGISM 


37 


SISM 


TS 

The  theory  of 

ited  (§  5).  ^^^^ 
stands   to-day 
left  it.     A  few 
Dints,  but  these 
rine.     In  deai- 
we  shall  first 
nirpose,  or  the 
We  shall  then 
ich  it  is  corn- 
nature  of  these 
|ry   to   discover 
to  obtain  valid 
lulitions    which 

llacy. 

that  syllogistic 

n-,  rather   than 

Its  object  is 
,vhich  thinkin.i; 
houghts  whicli 

as  to  compel 


*  assent.     The  ideas  which  it  uses  as  material  are  fixed 
by  having  been  expressed  in  language.     Indeed,  it  is 
largely  with  words,  as  the  expression  of  thoughts,  that 
syllogistic  logic  deals.     Many  of  the   discussions  with 
which  it  is  occupied  have   reference  to  the  meanings 
S^of  words  and  propositions  ;  and  the  rules  which  it  fur- 
nishes may  be  taken  as  dirccl!ons  for  putting  together 
Ipropositions  in  such  a  way  as  to  lead  to  a  valid  conclu- 
"psion.     Nevertheless,  it  is  important  to  remember  that 
"tthese  rules  are  not  arbitrary  and  external,  but  find  their 
■justificatio-i    in   the    nature    of    thought.     Indeed,    the 
;,theory  of  the  .syllogism,  when  rightly  understood,  may 
§be  said  co  reveal  the  fundamental  characteristics  of  the 
>|process  of  intelligence.     For  it  brings  together    facts 
in  such  a  way  as  to   make  evident  their  relation    and 
|de{)endence.     It  connects  a  judgment  with  the  grounds 
lor  reasons  which  support  it,  and  is  thus  a  process  of 
^^ystcmatization.     In    order   to    understand   the    signifi- 
:ance    of   the   rules   of   syllogistic    logic,   then,   it    will 
frequently   be    necessary    to    look    beyond    words    and 
>r()positions  to  the  act  of  thought  whose   result  they 
;xj)rcss. 

A  great  deal  has  been  written  regarding  the  princi- 

)les,  or  laws  of  thought,  which  are  employed  in  syllo- 

'Histic  reasoning.     It  seems  better,  however,  to  postpone 

le  definite  consideration  of  this  subject  until  the  student 

las  learned  more  about  the  various  kinds  of  syllogisms, 

bd  has  had  some  practice  in  working  examples.     In 

lealing  with  the  nature  and  principles  of  thought  in  the 

lird  part  of  this  book,  it  will  be  necessary  to  discuss 

lis  question  at  length.     lu'en  at  the  present  stage  of 


I 


38 


THE   SYLLOGISM   AND   ITS   PARTS 


our  inquiry,  however,  it  is  important  to  notice  that  syl- 
logistic reasoning  presupposes  certain  simple  and  fun- 
damental principles  of  thought  whose  nature  we  shall 
have  to  examine  hereafter.  In  particular,  the  regular 
syllogism  is  founded  on  a  principle  v/hich  we  may  call 
the  law  of  Identity,  or  the  law  of  Contradiction,  according 
as  it  is  stated  affirmatively  or  negatively.  Stated  affirm- 
atively, this  so-called  *  law '  simply  expresses  the  fact 
that  every  term  and  idea  which  we  use  in  our  reason- 
ings must  remain  what  it  is.  A  is  A,  or  has  the  same 
value  and  meaning  wherever  emploved.  The  law  of 
Contradiction  expresses  the  same  thing  in  negative 
language.  A  cannot  be  both  B  and  not  B.  If  any 
term  is  taken  to  be  the  same  as  another  in  one  connec- 
tion, it  must  always  be  taken  to  be  so ;  if  it  is  different, 
this  relation  must  everywhere  be  maintained.  The 
data  or  materials  which  are  employed  in  the  syllogism 
are  ideas  whose  meaning  is  supposed  to  be  perma- 
nently fixed,  and  expressed  in  words  which  have  been 
carefully  defined.  It  would  be  impossible  to  reason,  or 
to  determine  the  relation  of  our  ideas,  if  their  mean- 
ing were  to  change  without  notice,  or  if  the  words  by 
means  of  which  they  are  expressed  were  used  now  in 
one  sense,  and  now  in  another.  It  is  of  course  true 
that  our  ideas  regarding  the  nature  of  things  change 
from  time  to  time.  And,  as  is  evident  from  one's  own 
experience,  as  well  as  from  the  history  of  language,  a 
corresponding  change  takes  place  in  the  meaning  of 
words.  But  the  assumption  upon  which  syllogistic 
reasoning  proceeds,  is  that  the  ideas  which  are  to  be 
compared  are  fixed   for  the   mean  time,  and  that  the 


§  lo.    THE   TARTS  OF  A  SYLLOGISM 


39 


at  syl- 

d  fun-               > 

-  shall 

-egular                - 
ay  call 
wording 

affirm- 

tie  fact 

reason-              | 

•J 

e  same 

law  of              1 

* 

legative              % 

If  any              '. 

'    1 
connec-             | 

ifferent,             i 

.      The            1 

^llogism              1 

perma-              1 

/e  been              | 

Lison,  or             1 

mcan- 

ords  by 

now  in 

se  true 

change 

e's  own 

uage,  a 

ning  of 

Uogistic 

te  to  be 

hat  the 


words  by  which  they  are  expressed  are  used  in  the 
same  sense  throughout  the  course  of  the  argument. 
In  this  kind  of  reasoning,  then,  just  as  in  geometry,  it 
is  essential  that  the  terms  which  enter  into  the  argu- 
ment be  clearly  and  precisely  defined,  and  that  when 
thus  determined  they  shall  be  taken  as  fixed  and  un- 
changeable until  further  notice  is  given. 

It  is  quite^  possible  that  all  the  requirements  of  the 
syllogism  may  be  met  without  its  conclusions  being 
true  of  reality.  In  other  words,  an  argument  may  be 
fonnally  true,  but  really  false.  It  is  not  dif^cult  to 
understand  why  this  may  happen.  The  syllogism  ac- 
cepts the  ideas  and  judgments  which  it  compares  with- 
out criticism.  These  data  are  of  course  the  product  of 
previous  acts  of  thinking.  But  in  proceedmg  to  ar- 
range them  in  syllogistic  form,  we  do  not  inquire 
whether  or  not  they  are  true ;  i.e.  adequate  to  express 
the  nature  of  the  things  for  which  they  stand.  For 
the  purposes  of  the  syllogism  it  is  only  essential  that 
their  meanings  be  clearly  understood,  and  that  these 
meanings  be  regarded  as  fixed  and  permanent. 

§  10.  The  Parts  of  a  Syllogism. — The  syllogism  may 
be  said  to  express  a  single  comprehensive  act  of  thought. 
We  may  define  inference  as  a  judgment  which  has  been 
expanded  so  as  to  exhibit  the  reasons  by  which  it  is 
supported.     In  the  syllogism 

.Tlie  geranium  has  five  pointed  sepals, 
vThis  plant  has  not  five  sepals, 
'Therefore  it  is  not  a  geranium. 

we  may  cay  that  we  have  the  judgment,  'this  plant  is 


P 


40 


THK   SYLLOGISM   AND    ITS    I'ARTS 


h: 


^^ 


i 


not  a  geranium,'  supported  by  the  propositions  which 
precede  it,  and  that  the  whole  syllogism  taken  together 
expresses  a  single  thought,  which  is  complete  and  self- 
sufficient.  It  is  jDossible,  however,  even  when  one  is 
dealing  directly  with  the  process  of  thinking,  to  dis- 
tinguish in  it  different  subordinate  steps,  various  stages 
which  serve  as  resting  places,  in  the  course  of  its  passage 
to  the  complete  and  comprehensive  form  represented 
by  the  syllogism.  But  it  is  usual,  in  dealing  with  the 
syllogism,  to  take  a  more  external  view  of  its  nature, 
and  to  regard  it  primarily  as  made  up  of  words  and 
propositions. 

In  this  sense,  a  syllogism  can,  of  course,  be  divided 
into  parts.  In  the  first  place,  it  is  composed  of  three 
propositions.  In  the  example  given  above  the  two 
propositions  which  stand  first  are  called  the  premises, 
since  they  furnish  the  grounds  or  reasons  for  the  propo- 
sition which  stands  last,  and  which  is  known  as  the 
conclusion.  However,  it  is  not  true  that  we  always 
find  the  two  premises  and  the  conclusion  arranged  in 
this  regular  order  in  syllogistic  arguments.  Oftentimes 
the  conclusion  is  given  first.  Frequently,  too,  one  of 
the  premises  is  not  expressed,  and  has  to  be  supplied  in 
order  to  complete  the  argument.  Thus  the  statement, 
'  he  must  be  more  than  sixteen  years  of  age,  for  he 
attends  the  university,'  is  an  incomplete  syllogism. 
The  conclusion,  as  will  be  readily  seen,  stands  first. 
There  is  also  only  one  premise  expressed.  To  put  this 
statement  in  the  regular  syllogistic  form  we  have  to 
supply  the  missing  premise  and  arrange  it  as  fol- 
lows :  — 


M 


I 


§  lo.    THE   PARTS   OF  A   SYLLOCISM 


41 


IS  which 
together 
and  sclf- 
n  one  is 
J,  to  dis- 
is  stages 
3  passage 
)resented 
with  the 
s  nature, 
ords  and 

e  divided 
of  three 
the  two 
premises, 

he  propo- 
^n  as  the 
e  always 
ranged  in 
ftentimes 
o,  one  of 
jp  plied  in 
tatement, 
e,  for  he 
syllogism, 
mds  first. 
)  put  this 
:  have  to 
It   as   fol- 


-ig 


All  .students  of  the  university  arc  nio'v  tiian  sixteen  years  of  age, 

He  is  a  student  of  the  university, 

Therefore  he  is  more  than  sixteen  years  of  age. 

When  one  premise  of  an  argument  is  lacking,  the  name 
of  cnthymtme  is  applied  to  it.  This  term  is  derived  from 
the  two  Greek  words  (eV  Ovfifo),  signifying  '  in  the  mind,' 
the  missing  premise  being  regarded  as  in  consciousness, 
though  no^  expressed.  It  is  of  great  importance  to  form 
the  habit  of  making  clear  to  oneself  the  premises  by 
which  any  conclusion  claims  to  be  supported.  In  this 
way  groundless  assumptions  are  often  brought  to  light, 
and  the  weakness  of  an  argument  exposed.  Whenever 
words  like  'therefore,'  'for,'  'because,'  'it  follows,'  etc., 
are  u.sed  in  their  proper  signification,  it  is  possible  to 
find  an  argument  composed  of  two  premises  and  a  con- 
clusion. But  one  must  not  allow  oneself  to  be  imposed 
upon  by  the  mere  words,  but  must  insist  on  understand- 
ing exactly  what  are  the  premises  in  the  case,  and  how 
the  conclusion  follows  from  them. 

It  is  possible  to  carry  the  division  of  a  syllogism  still 
further.  Every  logical  proposition  may  be  divided  into 
two  terms,  and  a  copula  or  connecting  link.  The  terms, 
which  are  the  extremes  of  the  proposition,  are  named 
the  subject  and  the  predicate.  Thus  in  the  proposition, 
'the  fields  are  covered  with  snow,'  'the  fields'  is  the 
subject,  '  are,'  the  copula,  and,  '  covered  with  snow,' 
the  predicate.  To  reduce  a  proposition  to  the  logical 
form  in  which  it  is  most  conveniently  treated,  it  is  neces- 
sary to  express  it  in  such  a  way  that  the  two  terms  are 
united  by  some  part  of  the  verb  'to  be,'  preferably  'is' 
or  '  are.'     Thus  the  sentence,  '  No  plant  can  grow  with- 


^1 


42 


TIIK   SYLLOGISM    AND    ITS   PARTS 


\{ 


'i 


out  light  and  heat,'  would  be  expressed  as  a  logical 
proposition  in  the  following,  or  some  similar,  form  :  '  No 
plant  is  an  organism  which  can  grow  without  light  and 
heat.'  *  Men  have  strong  passions,'  may  be  written, 
'  Men  arc  beings  having  strong  passions.'  It  is  always 
well  to  reduce  a  sentence  to  some  such  form,  by  substi- 
tuting for  the  verb  of  predication  some  part  of  the  verb 
•to  be.' 

The  analysis  of  the  syllogism  gives  us  the  divisions 
under  which  it  is  convenient  to  treat  this  part  of  logic. 
We  shall  accordingly  deal  (i)  with  Terms,  (2)  with 
Propositions,  and  (3)  with  the  Syllogism  as  a  whole. 

These  divisions,  however,  are  only  made  for  the  sake 
of  convenience  in  treatment.  It  must  not  be  forgotten 
that  a  term  is  a  part  of  a  proposition.  To  understand 
the  nature  of  a  term,  it  is  necessary  to  consider  the 
part  which  it  plays  in  the  judgment  which  the  propo- 
sition expresses.  In  other  words,  the  function  of  the 
term,  rather  than  the  form  of  the  word  or  words  em- 
ployed, must  be  considered.  It  is,  of  course,  tru"  hat 
we  naturally  and  commonly  use  certain  word  forms  cO 
express  certain  kinds  of  ideas,  just  as  in  the  grammati- 
cal sentence  the  different  'parts  of  speech', —  nouns, 
verbs,  etc.,  —  have  each  a  definite  and  comparatively 
permanent  function.  But  even  in  the  sentence,  it  is  the 
part  which  the  word  in  its  grammatical  function  plays, 
rather  than  its  form,  which  determines  whether  it  is  to 
be  classified  as  a  noun  or  an  adjective,  a  preposition  or 
a  conjunction.  In  dealing  separately  with  terms,  as  we 
propose  to  do  in  the  next  chapter,  we  shall  be  occupied 
to  a  large  extent  with  the  form  of  ivords  in  which  cer- 


;'l  ■ 


§  II.    rROl'USED    DIVISION   Ol-    MENIAL   Ol'ERA'riONS       43 


a  logical 
rm :  '  No 
ight  and 

written, 
is  always 
)y  substi- 

the  verb 

divisions 
of  logic. 
(2)  with 
^hole. 
the  sake 
forgotten 
iderstand 
Isidor  the 
le  propo- 
>;/  of  the 
ords  em- 
rir    hat 
orms  cO 
rammati- 
—  nouns, 
aratively 
it  is  the 
)n  plays, 
r  it  is  to 
sition  or 
is,  as  we 
occupied 
ich  cer- 


tain kinds  of  ideas  are  usually  expressed.  But,  as  the 
same  word  or  group  of  words  may  be  used  tor  different 
purposes,  it  will  be  necessary,  in  order  to  understand 
the  meaning  of  terms,  to  refer  frequently  to  the  various 
ways  in  which  they  are  used  in  a  proposition. 

The  same  difficulty  exists  when  propositions  are  con- 
sidered by  themselves,  the  relation  to  the  complete 
argument  of  which  they  form  a  part  being  thus  ig- 
nored. In  this  case,  however,  the  results  of  the  isola- 
tion are  not  so  apparent,  for  a  proposition  forms,  in 
a  certain  sense,  a  whole  by  itself.  It  is  the  expression 
of  a  judgment  which,  as  we  shall  see  later,  is  the  unitary 
process  of  thought.  It  has  thus  a  significance  of  its 
own,  as  expressing  a  more  or  less  complete  and  inde- 
pendent act  of  thought.  Nevertheless,  it  must  not  be 
forgotten  that  it*^  independence  and  completeness  are 
only  partial  and  relative.  A  single  proposition  cannot 
.stand  alone.  Taken  strictly  by  itself,  a  proposiiion  is 
only  a  fragment.  In  order  to  make  it  intelligible,  it 
must  be  brought  into  relation  with  the  other  proposi- 
tions which  state  the  grounds  or  reasons  upon  which 
it  rests,  or  the  conclusion  which  it  helps  to  support. 
The  logical  nature  of  a  proposition  will,  therefore,  de- 
pend upon  its  function  in  an  argument,  and  in  treating 
of  propositions  this  fact  must  not  be  forgotten. 

§  II.    The  Proposed  Division  of  Mental  Operations. — 

It  is  frequently  stated  in  text-books  on  logic  that  corre- 
sponding to  the  division  into  Terms,  Propositions,  and 
Syllogisms,  there  must  be  a  division  of  the  different  kinds 
of  thought,  or  of  operations  of  the  mind.     These  differ- 


I 


a 


44 


TIIK   SYLLOGISM    AND   ITS   PARTS 


cnt  operations  arc  usually  called  Simple  Apprehension, 
Judgment,  and  Reasoning.  "The  first  of  these,  Simple 
Apprehension,  is  the  act  of  mind  by  which  \vc  merely 
become  aware  of  something,  or  have  a  notion,  idea,  or 
impression  of  it  brought  into  the  mind.  The  adjective 
simple  means  apart  from  other  things,  and  apprehension^ 
the  taking  hold  by  the  mind.  Thus  the  name  or  term 
'  iron '  instantaneously  makes  the  mind  think  of  a  very 
strong  and  very  useful  metal,  but  does  not  tell  us  any- 
thing about  it,  or  compare  it  with  anything  else."  ^ 
Judgment,  the  account  continues,  is  an  entirely  dif- 
ferent action  of  mind,  and  comes  later  than  Simple 
Apprehension.  It  consists  in  comparing  two  notions 
or  ideab  djrived  from  simple  apprehension  in  order  to 
ascertain  whether  they  agree  or  differ.  In  order  to 
judge,  we  must  have  two  notions  or  ideas  ready  in  the 
mind.  The  jud^mient  results  from  comparing  these, 
and  affirming  tliat  they  agree  or  do  not  agree.  In 
the  same  way,  having  already  made  judgments,  we 
can  combine  them  into  arguments  or  processes  of 
reasoning  by  a  new  and  still  different  activity  of  mind. 
Apprehension,  judgment,  and  reasoning  arc  thus  sup- 
posed to  be  separate  and  distinct  mental  operations. 
It  is  true  that  the  later  forms  employ  as  their  mate- 
rial the  finished  products  of  the  earlier.  But  from  this 
point  of  view,  apprehension,  judgment,  and  reasoning 
simply  succeed  one  another.  The  real  unity  which 
belongs  to  these  operations  ar-  forms  qI  intelligen'^e  is 
not  set  forth. 


^  j'evons,  Lessons  on  l.ir^ic,  pp.  ii,  12. 


rchcnsion, 
sc,  Simple 
,ve  merely 
n,  idea,  or 
;  adjective 
irchcnsion, 
le  or  term 
of  a  very 
2II  us  any- 
ig   else."^ 
tirely   dif- 
m    Simple 
IV)   notions 
n  order  to 
\  order  to 
ady  in  the 
ng    these, 
gree.      In 
Tients,   we 
)cesses    of 
of  mind, 
thus  sup- 
perations, 
leir  mate- 
from  this 
reasoning 
ity   which 
ligen^e  is 


I 


§11.    I'KOI'OSKP   pIMSION   or   .MKNTAL  ol'KRATlONS       45 

The  whole  of  Part  III.  of  the  present  book  may  be 
regarded  as  an  argument  against  this  point  of  view. 
We  shall  there  endeavour  to  show  that  thinking  is  not 
a  i)rocess  of  externally  joining  on  part  to  part,  but 
consists  in  a  development  or  expansion  of  knowledge 
from  within.  And,  in  particular,  we  shall  try  to  ex- 
hibit the  essential  unity  of  intellectual  processes  by 
whatever  name  they  may  be  called,  and  at  whatever 
stage  of  development  they  may  be  found.  Without 
anticipating  too  far  our  future  discussions,  we  may  point 
out  that  the  primary  process  of  thon.ght  is  not  'Simple 
Ai)prehension,'  but  Judgment.  In  other  words,  it  is 
ini]iossible  to  apprehend  or  passively  receive  ideas. 
'To  get  an  idea,'  or  to  understand  the  meaning  of  a 
term,  is  only  possible  when  the  mind  judges  or  inter- 
prets things  for  itself.  To  have  an  idea  or  concept 
of  anything,  then,  is  to  be  able  to  judge  more  or  less 
clearly  and  confidently  regarding  it.  I  have  an  idea 
of  'iron'  when  I  judge  that  it  is  'black'  and  'heavy' 
and  'malleable.'  And  the  more  complete  and  exact  we 
can  make  our  judgments,  the  better  is  the  idea  or  appre- 
hension which  we  obtain  of  the  thing  in  question.  In- 
telligence or  thought  must  not  be  regarded  as  at  first 
merely  receptive.  It  does  not  beg'.n  by  laying  hold  of 
separate  ideas  or  terms,  and  afterwards  call  in  judg- 
ment as  a  new  kind  of  process  to  bring  the  former 
into  relation.  But  it  is  from  the  first  a  systematizing 
and  relating  activity  which  proceeds  from  the  less 
perfect  to  the  more  perfect  form  of  judgment. 


CHAPTER   IV 


THK    VARIOUS    KINDS    OF    TERMS 


§  12.  Singular,  General,  and  Collective  Terms.  —  A 
logical  term,  as  wc  have  already  seen,  is  an  clement  of 
a  proposition.  In  dealing  with  terms  apart  from  prop- 
ositions, we  shall  be  concerned  mainly  with  different 
classes  of  words  and  the  meanings  which  they  usually 
express.  It  will  be  impossible,  however,  to  fix  the 
meanings  of  terms  absolutely  without  reference  to  the 
way  in  which  they  are  used  in  propositions.  The  first 
division  which  we  have  to  notice  is  that  into  Singular  or 
Individual,  General,  and  Collective  terms. 

(i)  A  Singular  or  Individual  term  is  one  which  can 
be  applied  in  the  same  se^.^e  to  but  a  single  thing. 
The  main  purpose  of  Singular  terms  is  to  refer  to, 
<Tr  identify,  some  individual  object.  Proper  names  are 
all  singular.  It  is  true  that  proper  names  are  some- 
times used  to  denote  a  class  of  objects,  as,  c.j^.,  *  a 
Daniel,'  '  a  Mephistopheles.'  But  when  thus  employed 
they  lose  their  real  character  as  proper  names.  That 
is,  their  function  is  no  longer  merely  to  identify  certain 
individuals  by  naming  them,  but  to  describe  them  by 
mentioning  certain  qualities  or  characteristics  which 
they  are  supposed  to  possess.  But  the  ordinary  pur- 
pose in  using  a  proper  name  is  to  indicate  some  indi- 
vidual to  whom  the  name  belongs.  In  this  sense,  then, 
proper  names  are  Singular. 

46 


\   ■  \ 


■Jt 


§  12.   SINdULAK.  GKNKRAI.,  AXl)  COLLECTIVE  TERMS       47 


erms.  —  A 

element  of 
rom  prop- 
i  different 
icy  usually 
to  fix  the 
ticc  to  the 
The  first 
lingular  or 

which  can 
Lde  thing, 
refer  to, 
names  are 
are  some- 
is,  ^,^.,  *a 

employed 
Hes.     That 

fy  certain 
them  by 
ics  which 
inary   pur- 

ome  indi- 

mse,  then, 


I  In  addition,  any  word  or  group   of   words   which  is 

applied  to  a  single  thing  may  l)e  regarded  as  singular. 

I  And  i)y  'single  thing,'  we  mean  anything  which  is 
thought  of  as   one,  as   well   as  objects   which  are   per- 

}  celved  through  the  senses.  Thus,  'the  waterfall  just 
below  the  bridge,'  'the  centre  of  the  earth,'  are  singu- 
lar terms,  and  so  also  are  words  like  'justice,'  'good- 
ness,' 'the  chief  end  of  man.'  It  is  perhaps  more 
doubtful  whether  we  should  call  terms  such  as  'white- 
ness,' 'sweetness,'  singular,  since  we  speak  of  differ- 
'  ent  degrees  and  kinds  of  whiteness  and  sweetness. 
The  (jucstion  would  have  to  be  decided  in  every  case 
by  reference  to  the  way  in  which  the  terms  are  em- 
ployed in   i)ropositions. 

(2)  A  General  term  is  a  name  which  ap[:)lies  to  a 
whole  group  of  objects.  It  is  not  limited,  like  the  sin- 
gular name,  to  a  single  thing,  but  applies  to  a  number 
of  different  things.  All  class  names  like  '  metal,' 
'  man,"  '  works  on  logic,'  are  of  this  character.  The 
general  name  belongs  to  each  and  every  individual 
of  a  whole  class.  Thus  iron,  gold,  silver,  etc.,  are 
'metals';    and  A,  B,  and  C,  'men.' 

(3)  A  Collective  term,  on  the  other  hand,  is  a  name 
applied  to  a  number  of  indixiduals  when  taken  together 
and  treated  as  a  whole,  as  'an  army,'  'an  audience.' 
It  is  important  to  distinguish  carefully  between  general 
and  collective  terms.  A  general  term  is  a  name  which 
applies  equally  to  each  individual  of  the  group ;  or,  in 
other  words,  it  is  used  of  the  individuals  distrihutivcly. 
A  collective  name  belongs  to  the  whole,  but  not  to  the 
separate  parts  of  the  whole.     Thus  we  say  that   '  sol- 


\  r.-       . 

H 


4« 


Tlir:   VAKlol'S    KIN'DS  OF  TKUMS 


h 


'ir  \ 


1^ 


dicr  '  is  ;i  ^^ciicral  niimc,  and  is  used  distribiitivcly  of 
each  iium  in  a  rc<;imcnt.  '  Regiment,'  however,  is  a 
collective  name,  lor  it  applies  only  to  the  whole  group, 
and  not  to  the  individual  soldiers. 

Ambiguity  sometimes  arises  from  the  fact  that  the 
ICnglish  word  *  all '  is  used  in  both  of  these  senses. 
That  is,  it  may  mean  'all  taken  together,'  or  'each  and 
every.'  Thus  we  can  say :  '  All  the  angles  of  a  tri- 
angle are  less  than  two  right  angles';  and  'all  the 
angles  of  a  triangle  are  equal  to  two  right  angles.'  In 
the  former  sentence,  the  wcrd  'all'  is  used  distribu- 
tively  ;  in  the  latter,  collectively.  In  Latin  two  different 
words  are  used  :  cuncti  expresses  the  collective  sense 
of  '  all,'  and  omncs  its  distributive  signification. 

It  is  worth  noticing  in  this  connection  that  it  is  the  use  wliich 
is  made  of  terms,  rather  than  the  fonii  of  the  words  composintf 
them,  which  determines  their  lojjjical  character.  TIius  terms  which 
are  collective  in  one  connection  may  be  general  in  another.  '  Re<;i- 
ment,'  for  example,  is  a  collective  term  with  reference  to  the  soldiers 
which  compos('  '»,  hnt  general  when  used  as  a  common  term  for  a 
number  of  similar  divisions  of  an  army.  The  same  is  also  true  of 
terms  like  'grove,'  'mob,'  'class,'  etc.  Again,  collective  terms 
may  be  very  properly  regarded  as  sintjular  when  the  j^roposition 
in  which  they  are  used  emphasizes  the  unity  and  .solidarit}'  of  the 
^roup.  A  proper  name  is  sometimes  applied  to  a  collection  of  in- 
dividuals that  are  permanently  united  or  that  have  acted  to,<i;ether 
on  sone  historic  occasion,  as,  for  example,  'The  F'ifth  Cavalry  regi- 
ment,' •■  The  Charge  of  the  Six  Hundred.' 


§  13.  Abstract  and  Concrete  Terms. — Terms  are  fur- 
ther divided  into  abstract  and  concj'cte  terms.  The 
word  '  abstract '  is  often  used  popularly  to  describe 
anything  which  is  difficult  to  understand,     r^tymologl- 


§  I  J.     AlJSrU.UI'  AND  aJNCKKlK    lllkMS 


49 


)utivoly  of 
I'cvcr,  is  a 
olc  group, 

t  that  the 
;se  senses, 
'each  and 
>  of  a  tri- 
c!  'all  the 
iiirles.'  In 
d  distribu- 
^o  different 
:tive  sense 
ion. 

lie  1/.U'  wliich 

Is  composing 

terms  which 

her.     '  Regi- 

)  the  soldiers 

n  term  for  a 

also  true  of 

ective    terms 

projiosition 

arity  of  the 

ection  of  in- 

ted  to.tjether 

Cavalry  regi- 

is  are  fiir- 
ms.  The 
describe 
i^tymologl- 


cally,  it  si^ndfies  drawn  off,  se|)arated  {abstrahoy  to 
draw  off,  take  away).  We  may  distin';uish  two  sen.ses 
in  which  the  word  is  used,  botii,  however,  being  derived 
from  its  etymological  signification. 

( I )  A  term  is  called  abstract  when  it  refers  to  some 
object  which  cannot  be  directly  perceived  throtigh  the  v 
1  se^iises^  and  concn'tc  when  su_ch^percei)tion  is  possible. 
Tiuis  'a  beech  tree,'  '  a  tall  man,'  'a  sweet  taste,'  being 
names  of  things  which  can  be  j)erceived,  are  concrete. 
Words  like  'sweetness,'  'hardness,'  etc.,  have  no  objects 
ol  sense  directly  corresponding  to  them,  and  are  for 
this  reason  called  abstract.  The  same  is  true  of  terms 
like  'individuality,'  'equality,'  'jii^stice,'  etc.  These 
words  represent  objects  of  thought,  rather  than  ob- 
jects of  sense.  There  may  be  cases  or  instances  of 
'equality,'  'justice,'  etc.,  which  fall  under  our  percep- 
tion, but  the  real  object  to  which  these  words  corre- 
spond is  not  a  thing  which  can  be  perceived  through 
the  senses  at  all.  Their  reality  is  conceptual,  or  for 
thought,  not  something  directly  revealed  through  the 
senses. 

It  is  important  to  notice  that  there  are  degrees  of  abstractness  in 
terms,  according  as  the  objects  for  which  they  stand  are  nearer  to,  or 
further  removed  from  ordinary  sense-perception.  All  general  or 
class  names  are  abstract.  One  cannot  point  to  a  single  object,  to 
which  the  term  'metal,'  for  e.xample,  or  the  term  '  man'  corresponds. 
But  although  such  terms  have  no  direct  sensuous  object,  yet  we  feel 
that  they  stand  nearer  to  sense-perception,  and  are  therefore  less 
abstract,  than  words  like  'animal,'  'inorganic  substance.'  These 
terms,  again,  are  perhaps  less  al)stract  than  'energy,'  or  'spirit,'  or 
even  than  singular  terms  like  'justice,'  'the  ground  of  the  universe,' 
etc. 

B 


:n.: 


I 


;l  ' 


I 


i 


50 


'II  IK    VAKIOLS    KINDS    I H'    TKKMS 


t 


ji'i 


(2)  Again,  the  word  '  al)stract '  is  applied  to  any  ob- 
ject which  is  treated  apart  Irom  the  whole  to  which  it 
belongs.  Thus  it  would  be  an  abstraction  to  attempt 
to  represent  the  nature  ot"  a  leaf  in  complete  isolation 
from  the  plant  to  which  it  belongs,  or  to  consider  the 
nature  of  a  man  without  regard  to  the  social  institu- 
tions—  family,  church,  state,  etc.  —  of  which  he  is  a 
member.  Of  course,  it  is  essential  when  dealing  with  a 
complex  whole  to  analyze  it  into  its  parts,  and  to  under- 
stand just  what  is  the  nature  of  each  })art  when  taken 
by  itself.  But  in  order  to  comprehend  fully  the  nature 
of  the  parts,  it  is  necessary  to  restore  them  to  their 
proper  setting,  and  to  see  their  relation  to  the  concrete 
whole.  In  this  sense  of  the  word,  then,  'abstract' 
applies  to  what  i:  taken  out  of  its  pxopcr.  setting,  broken 
off,  and  considered  apart  from  the  things  to  which  it  is 
organically  related..  Concreie.  on  the  other  hand,  means 
what  is  whole  and  complete,  a  system  of  things  which 
mutually  support  and  explain  one  another. 

Since  science  has  to  analyze  things  into  their  elements, 
and  to  investigate  and  describe  these  elements  in  detail, 
it  is  impossible  entirely  to  avoid  abstraction.  But  it  is 
necessary,  in  order  to  completely  understand  the  nature 
of  a  complex  object,  that  the  abstractions  of  analysis 
shall  be  corrected.  In  other  words,  the  concrete  rela- 
tions in  which  things  st.tud  must  not  be  ignored  in 
investigating  them.  The  conception  ot  evolution  in 
recent  times  has  done  much  to  render  the  biological 
sciences  more  concrete  in  the  sense  in  which  we  are 
now  using  the  term.  For  it  has  substituted,  for  the  old 
method  of  treating  each  species  of  plant  and  animal  as 


I 


V         ( 


Al{S'lkA(  r    AND   CONCRKTE  TERMS 


51 


to  any  ob- 
;()  wliich  it 
to  attempt 
tc  isolation 
onsider  the 
:ial  institu- 
:h  he  is  a 
iliiiG;  with  a 
d  to  under- 
,vhen  taken 

the  nature 
m  to  their 
lie  concrete 

'  abstract ' 
in  IT,  broken 

which  it  is 
and,  means 
ings  which 

r  elements, 
s  in  detail, 

But  it  is 
the  nature 
d(  analysis 
Crete  rela- 
i^nored  in 
ulution    in 

biological 
ch  we  are 
for  the  old 

animal  as 


■S 


distinct  and  sejxiratc,  'cut  off  from  each  other  as  if  by 
a  hatchet,'  the  view  that  all  organic  beings  are  members 
of  one  family,  and  can  be  properly  understood  only  in 
their  relations  to  one  another. 

It  is  interestin<;  10  notice  that,  fioin  this  jioint  of  view,  sense- 
pcrccption  is  more  abstract  than  thought.  For  the  senses  represent 
thiiij^s  in  isolation  from  each  other.  Each  thing  is  known  in  sense- 
percejition  as  a  separate  indiviihial,  occupying  its  own  space  and 
time,  and  in  tliis  way,  cut  off  from  its  fellows.  It  is  the  business  o' 
thought,  on  tlie  other  hand,  to  discover  the  relatit)ns  between  things, 
and  the  principles  according  to  which  they  are  united.  Thinking 
thus  overcomes  tlie  abstract  point  of  view  of  sense-perception  by 
showing  that  what  apjiear  to  the  latter  as  separate  oljjects  are 
really  closely  and  necessarily  connected  as  members  of  a  com- 
mon unity  or  sysiein.  Each  science  takes  as  its  province  certain 
facts  which  resemble  one  another,  but  which  nevertheless  ajipear 
to  sense-perception  to  be  cjuiie  independent.  It  attempts  by 
thinking  to  bring  these  facts  into  relation,  to  show  that  they  are 
all  cases  of  some  law,  that  there  is  a  common  princijjle  which  unites 
them  as  parts  of  a  whole  or  .system.  The  law  of  gravitation,  for 
example,  e.vpresses  the  unity  whica  thought  has  discovered  in 
things  which  appear  to  .sense-perception  as  difterent  as  the  falling 
of  an  apple,  the  movements  of  the  heavenly  bodies,  and  the  ebb 
and  flow  of  the  tides.  Scientific  knowledge,  then,  is  more  con- 
crete than  the  facts  which  we  learn  from  ordinarv  sense-percep- 
tion, because  it  brings  to  light  real  unity  and  connection  in  facts 
which  appear  to  be  entirely  isolated  and  independent  from  the 
latter  point  of  view. 

In  employing  the  terms  'Abstract'  and  'Concrete'  it 
is  of  the  utmost  importance  to  distinguish  the  two  sig- 
nifications of  the  words.  From  one  point  of  view,  as  wc 
have  seen,  all  thought  terms  are  abstract,  as  opposed  to 
words  which  refer  directly  to  objects  of  sense-i)erccption. 


i 


!■ 


52 


Tilt:   VARIOUS    KINDS   OF  TERMS 


In  another  sense,  'abstract'  denotes  wliat  is  j)artial  and 
incomi)lete,  what  is  taken  l)\  itself  and  out  of  relation 
to  the  system  of  tnings  to  which  it  belongs.  And  since 
the  real  connection  and  relations  of  things  are  not  given 
by  perception,  but  have  to  be  discovered  by  thought, 
the  knowledge  which  the  latter  yields  is  more  concrete, 
in  this  latter  sense  of  the  term,  than  that  afforded  by 
the    jrmer. 


§  14.  Positive  and  Negative  Terms. — The  distinction 
between  Positive  and  Negative  terms  is  very  obvious. 
Positive  terms  express  the  existence  of  some  quality,  or 
group  of  qualities,  in  the  objects  which  they  denote;  as, 
e.g.,  '  happy,'  '  good,'  '  equality,'  *  organism,'  etc.  A  Neg- 
ative term,  on  the  other  hand,  indicates  the  absence 
of  qualities  or  properties  in  some  object;  'bad,'  'un- 
happy,' 'inorganic,'  'injustice,'  for  example,  arc  negative 
terms.  Negative  terms  are  often  formed  from  positive 
by  means  of  the  affix,  /ess,  as  in  '  hopeless,'  or  by  means 
of  certain  prefixes,  of  which  the  more  common  are  7tn,  in, 
(/is,  d,  anti.  Words  which  arc  positive  in  form  are,  how- 
ever, often  negative  in  meaning,  and  are  used  as  the 
contradictories  of  other  terms.  Thus  '  ignorant '  is 
generally  regarded  as  the  negative  of  '  learned,'  '  dark- 
ness '  is  the  negative  of  '  light,'  etc.  It  is  not  always 
])ossible,  however,  to  find  a  separate  word  to  express  the 
exact  opposite  of  every  positive  term.  Words  are  used 
primarily  to  express  the  presence  of  qualities,  and  the 
negative  idea  may  not  be  referred  to  so  frequently  as 
to  require  a  separate  word  to  express  Jt.  Thus  there 
is  no  independent  term  to  express  the  opposite  of  '  trans- 


ij  in»   ixifisimmiiimimm 


lartiul  and 
)f  relation 
And  since 
not  given 
^  thought, 
I  concrete, 
forded  by 


distinction 

y  obvious. 

quality,  or 

enotc ;  as, 

c.    A  Neg- 

c  absence 

bad,*   *  un- 

c  negative 

m  positive 

by  means 

are  ////,  ///, 

are,  how- 

d  as  the 

orant '    is 

d,'  'dark- 

ot  always 

press  the 

are  used 

,  and  the 

uently  as 

lus  there 

of  '  trans- 


I 


§  14.     POSITIVE  AND   NEGATIVE  TERMS 


53 


f 


fcrable,'  but  by  employing  '  not*  as  a  negative  prefix  we 
obtain  '  not-transferable.' 

It  is  always  advisable  when  we  wish  to  limit  a  term  strictly  to  its 
negative  application  to  emjjjoy  ;/r'/  or  f/o//  as  a  prefix.  Words 
which  arc  negative  in  form  frequently  have  a  more  or  less  definite 
positive  signification.  Jevons  points  out  that  words  like  *  unloosed' 
and  'invaluable,'  though  negative  in  form,  have  a  positive  meaning. 
lUit,  in  addition,  terms  like  'unhappy,'  'immoral,'  do  not  merely 
indicate  the  absence  of  positive  qualities,  but  also  express  some 
positive  properties  of  the  objects  to  which  they  are  applied.  We 
speak  of  a  person  '  being  positively  unhappy ' ;  and  we  employ 
'non-moral'  to  express  the  simple  negative  relation  rather  than 
'immoral.' 

On  the  other  hand,  there  are  certain  terms  which  are  positive  in 
form  that  express  the  absence  of  qualities  or  attributes.  Words  like 
'blind,'  'dumb,'  'maimed,'  'orphaned,'  may  be  given  as  examples. 
These  are  often  called  Primitive  terms,  rather  than  Negative,  the 
distinction  being  that  they  refer  to  qualities  or  attributes  which  the 
objects  to  which  they  are  applied  naturally  and  usually  have,  but  of 
which  they  have  bee  ■'.  deprived,  or  which  they  have  never  possessed. 
Thus  '  blind,'  as  applied  to  a  man,  imjilies  that  he  has  lost  or  is  desti- 
tute of  the  ability  to  see  which  naturally  belongs  to  a  human  being. 

Again,  other  terms  seem  to  be  positive  and  negative  solely  in 
relation  to  each  other.  'Element'  and  'compound'  are  related 
negatives  or  contradictories.  It  is  difficult,  however,  to  say  which 
term  is  in  itself  negative  or  positive. 

It  is  important  to  notice  the  distinction  between  tlie^ 
relation  in  which  positi^Hi^and  negative  terms  stand  to 
each  other,  and  that  expressed  by  words  which  have 
to  do  with  opposite  extremes  of  something  which  pos- 
sesses quality  or  degree.  Po.sitive  and  negative  ternia, 
are  mutually  contradictory.  An  element  is  what  is  ;/ot 
a  compound,  'dishonest'  is  the  contradictory  of  'honest,' 


54 


TIIK   VARIOUS   KINDS   OK  TKRMS 


\J 


and  as  contradictories  there  is  no  middle  ground  be- 
tween them.  What  is  not  an  element,  is  a  non-element 
or  a  compound.  Opposite  or  contrary  terms,  on  the 
other  hand,  express  a  s;reat  difference  of  dej^rce  in  the 
objects  to  which  they  refer.  Thus  '  foolish '  is  the  op- 
])osite  of  '  wise,'  'cold  '  the  opposite  of  '  hot,'  and  '  bitter  ' 
oi  'sweet.'  ]^ut  there  is  always  the  possibility  of  a 
middle  <^round  between  oi)j)()sites.  We  cannot  say  that 
a  man  must  be  either  wise  or  foolish,  a  taste  either 
sweet  or  bitter.  The  logical  contradictory  of  '  wise  '  is 
'not-wise,'  of  'bitter,'  is  'not-bitter,'  etc.  (^pj)osite  or 
contrary  terms,  then,  must  be  carefully  distinguished 
from  contradictories. 


§  15.  Absolute  and  Relative  Terms. — Another  classi- 
fication of  terms,  which  is  usually  given  by  logicians, 
is  that  into  absolute  and  relative  terms.  An  absolute 
term  is  one  which  refers  to  an  object  which  exists  by 
itself,  and  has  an  intelligible  meaning  when  taken  alone. 
Thus,  'tree,'  'house,'  'the  State  of  New  York,'  are  ex 
amples  of  absolute  terms.  A  relative  term,  on  the  con- 
trary, is  a  nam  J  which  only  derives  a  meaning  from  its 
relation  to  something  else.  The  term  '  parent,'  for  ex- 
ample, cannot  be  thought  of  except  in  relation  to  'child.' 
Similarly,  '  teacher '  is  relative  to  'pupil,'  and  'cause'  to 
'effect.'  Relative  terms  usually  go  in  pairs  and  are 
known  as  Correlatives.  Adjectives,  as  well  as  nouns, 
may  be  related  in  this  way.  The  presence  of  one 
cpiality  or  characteristic  in  a  thing  frequently  implies 
the  presence  of  others.  Thus,  ignorance  and  super- 
stition, .sympathy  and  tolerance,  are  necessary  correla- 


nd  bc- 
;lenient 
on  the 
;  in  the 
the  op- 
'  bitter ' 
ty  of   a 
^ay  that 
c  cither 
wise '  is 
)osite  or 
iguished 


:r  classi- 

Doicians, 
absolute 

exists  by 
n  alone. 

'  are  ex 
the  con- 
froni  its 
;  for  ex- 
,, 'child.' 
ause'  to 
and   are 
s  nouns, 
of    one 
implies 
jd    su\)er- 
correla- 


§  ;6.     EXTHNSIOX    AM)    INTKXSIOX   UF   TKKMS  55 

tives,  because  the  one  involves  the  other,  or  is  invariably 
connected  with  it. 

It  is  of  course  true  tliat  no  tinitc  thing  is  completely  ai)S()hite  or 
independent  of  other  thuigs.  'Ihe  nature  of  everything  is  largely 
ileterndned  by  the  nature  of  the  other  things  with  which  it  stands 
in  relation.  A  tree,  for  exanii^le.  is  relative  to  the  seed  from  which 
it  s[)rang,  the  soil  in  which  it  grew,  tiie  sunshine,  rain,  etc.,  which 
accompanied  its  growth.  All  finite  things  have  a  beginning  and  an 
end.  and  are  also  intluenced  throughout  tlie  whole  period  of  their 
lives  by  the  action  of  othrr  things.  They  are  therefore  not  com- 
pletely absolute  ur  independent.  It  is,  however,  possil)le  to  make  a 
distinction  between  words  which  are  the  names  of  things  that  are 
comparatively  independent,  and  may  for  ordinary  purposes  be  con- 
sidered by  themselves,  and  those  which  h  i,'  e  only  a  meaning  when 
regarded  as  correlatives. 

§    16.    Extension    and    Intension    of    Terms.  ,s=»  In    the 

foregoing;  sections  of  this  chapter  we  have  explained 
the  nature  of  the  various  kinds  of  terms  with  which 
logic  deals.  It  is  now  necessary  to  notice  two  different 
purposes  for  which  terms  are  employed.  In  the  first 
place,  terms  are  used  tc  refer  to  things,  to  name  and 
identify  them.  Thtis  '  man '  refers  to  the  different 
individual  men,  John  Smith,  Thomas  Brown,  etc.,  as 
well  as  to  the  various  classes  of  men,  Caucasians, 
Indians,  Mongolians,  etc.  As  denoting  or  naming  ob- 
jects, whether  these  be  individual  things  or  classes  of 
things,  terms  are  said  to  be  employed  in  I'lxtension. 
But  words  are  also  used  to  describe  as  well  as  to  name. 
That  is,  they  represent  the  t[ualities  ov  attributes  be- 
longing to  things  for  which  they  stand.  They  are  not 
bare  names  without  signification,  but  as  the  ex])ression 


SC) 


'\'\\K   VARIOI'S    KINDS   OV  TKUMS 


h 


'I;  •'  < 

If'  > 


of  ideas  they  stand  for  certain  qualities  or  character- 
istics which  tliin_L!;s  are  judi^ed  to  i)()ssess.  '  Man,'  for 
example,  is  not  merely  a  name  which  may  be  applied 
to  individual  human  beings  or  races  of  men,  but  it 
implies  that  the  objects  so  named  have  certain  (lualities, 
such  as  animal  life,  reason,  and  the  power  of  com- 
municatin<^  with  their  fellows.  When  words  are  used 
in  this  way  to  defme  or  describe  thint;"s,  rather  than 
merely  to  name  them,  they  are  said  to  be  employed  in 
Intension, 

The  terms  "Denotation'  ami  •Connotation'  were  used  by  Mill 
instead  of  ICrtension  and  Intension,  respectively,  and  have  been 
adopteil  pretty  generally  since  his  time.  To  'denote,'  is  to  point 
out  or  specify  the  objects  for  wliich  a  term  stands  ;  and  to  'connote' 
is  to  tak';  account  of  the  attributes  or  qualities  which  a  name  implies. 
The  voids  'breadth,'  and  'comprehension,''  are  also  sometimes  used 
as  synonymous  with  Extension,  and  'depth,'  or  'content,'  instead  of 
Intension.  The  terms  U)  ])e  remembered,  however,  are  Extension 
or  Uenutu,tion,  and  Intension  or  Connotation. 

\  It  is  useful  to  accustom  ourselves  to  distinguish  these 
two  functions  or  uses  of  a  term,  —  to  notice,  that  is,  the 
things  or  classes  of  things  to  which  the  name  applies,  — 
and  also  to  reflect  upon  the  signification,  or  ways  of  judg- 
ing about  these  things,  for  which  the  name  stands.  The 
Extension  of  a  term,  as  has  been  said,  indicates  the 
objects  to  which  a  name  applies,  and  the  Intension  the 
qualities  or  attributes  which  it  signifies.  From  the  point 
of  view  of  extension,  therefore,  *  planet '  may  be  defined 
by  mentioning  the  names  of  the  various  planets,  Mer- 
cmy,  Venus,  the  Ivirth,  Mars,  etc.  Similarly,  a  term 
like  '  carnivora '  might  be  given  in  extension  by  nam- 


14 


11 


§  i6.     KXTF'.XSION    AM)    INTKXSIOX   ()F   TKRMS  57 


actcr- 
11,'  for  ' 
ppliccl 
but  it 
alitics, 
com- 
c  used 
r  than 
lycd  in 


by  Mill 
ive  l)cen 
to  point 
connote ' 
e  implies, 
mes  used 
instead  of 
Extension 


ih  these 
Lt  is,  the 
Iplies,  — 
I  of  judg- 
Is.     The 
ates  the 
Ision  the 
|he  point 
defined 
;ts,  Mer- 
,  a  term 
by  nam- 


Iul;  seals,  bears,  weasels,  dnL;s,  wolves,  cats,  lions,  etc. 
Usually,  howevtn*,  we  define  froni  the  point  of  view  of 
intension,  that  is,  by  statin,!;"  the  qualities  or  eharaeter- 
istics  for  which  the  term  stands.  Thus  we  ^ive  the 
intensive  meaning  of  'planet,'  as  a  heavenly  body  which 
revolves  in  an  ellijUical  orbit  round  the  sim.  *  Car- 
nivora,'  defined  from  the  same  point  of  view,  are  mam- 
malian vertebrates  which  feed  upon  tlesh.  It  is  not 
tmusual,  however,  to  supplement  an  intensive  definition 
by  turning  to  e.xtension  and  enimicrating  examples. 
Thus  we  might  add  to  the  definition  of  'carnivora'  just 
given,  the  words,  'as  lions,  tigers,  dogs,  etc' 

It  is  sometimes  said  that  the  intension  and  extension 
of  terms  vary  inversely.  This  is  simply  an  attempt  to 
give  a  mathematical  form  of  statement  to  the  fact  that 
the  more  a  term  is  defined,  or  limited,  by  the  addition  of 
attributes,  the  fewer  are  the  objects  to  vhich  it  applies. 
'  As  the  intension  of  a  term  is  increa.sed  its  extension  is 
diminished,  and  I'/a-  versa,'  is  the  form  in  which  the 
relation  is  ofteti  stated.  For  example,  let  us  begin 
with  some  class-name  like  '  animal,'  which  has  a  great 
extension,  and  add  a  new  attribute,  '  rational.'  We  get 
'rational  animal '<=  man.  This  term  now  ai-»i)lies  to  a 
much  smaller  number  of  individuals  than  'animal.'  The 
extension  of  the  former  term  has  been  diminished,  that 
is,  by  increasing  the  intension.  If  we  add  to  'man'  still 
another  attribute  like  'white,'  we  again  lessen  the  num- 
ber of  individuals  to  which  the  term  applies.  In  gen- 
eral, then,  it  can  be  seen  that  the  extension  of  a  term 
is  lessened  as  it  is  made  more  definite  by  the  addition 
of  new   attributes.      And,  conversely,  by  stripping  off 


--'  L 


5X 


riFi:  VAKInrs   kixds  of    TKiaiS 


'    i 


attributes,  by  'decreasing-  the  intension/  the  number 
ot  individuals  to  which  a  term  ai)i'l'es  is  increased. 
There  is,  however,  no  exact  ratio  l)etween  the  increase 
or  decrease  of  intension  and  the  corresponding  change 
in  extension.  Indeed,  the  extension  of  a  class  may 
increase  greatly  without  any  loss  of  intension  on  the 
part  of  the  term  by  which  the  idea  is  expressed.  Thus 
the  meaning  or  intension  of  the  term  'man'  has  not 
lost,  but  rather  gained,  during  the  last  hundred  years  by 
Mie  incrc'i'f  o*"     .p;;     loi-  throuf;hout  t!ie  woild. 

Extension  ^no  iMtv  -ion,  according  to  the  view  just 
given,  rej)resiMit  tv»;;  diff  '  nt  uses  or  functions  of  terms. 
Kvery  term  denotes  some  object  or  group  of  objects 
more  or  less  directly,  and  at  the  same  time  connotes  or 
signifies  certain  qualities  or  attributes.  Sometimes  the 
one  purpose,  sometimes  the  other,  is  the  pretlominant 
one  Proj)er  names,  for  example,  are  used  primarily 
to  denote  or  mark  out  things,  and  do  not  directly 
qualify  or  describe  them.  In  the  proposition,  'these 
animals  are  all  vertebrates,'  the  predicate  'term  'verte- 
brates '  is  employed  less  as  a  name  of  a  number  of 
animals,  than  as  a  description  of  tlieir  qualities.  Never- 
theless, in  both  these  cases  the  terms  employed  have  the 
double  function  of  naming  or  denoting  objects,  and  of 
connoting  qualities. 

Mill,  however,  and  certain  other  logicians  who  follow 
him,  make  a  distinction  between  connotative  and  non- 
connotative  terms.  "  A  non-connotative  term  is  one 
which  signifies  a  subj(,'ct  only,  or  an  attribute  only.  A 
connotative  term  is  one  which  denotes  a  sul)ject,  and 
implies  an  attribute.      By  a  subject  is  here  meant  any- 


i 


\i 


I?  «6. 


KXII-.NSJON    AM)    INTENSION    OT    TKKMS 


59 


imbcr 
:asc(l. 
:rcase 
lK)nfi;c 
1  may 
n\  the 
Thus 
as  not 
;ars  by 

:\v  just 
terms, 
objects 
lotes  or 
ncs  the 
jminant 
imarily 
lirectly 
' these 
'  verte- 
iber  of 
Never- 
ave  the 
and  of 

I)  follow 
[\d  non- 
is  one 
Inly.  A 
lect,  and 
lint  any- 


II 


thini<  which  possesses  attributes.  Thus  'John,'  or  '  Lon- 
don,' or  '  I'ji^dand  '  are  names  which  si.^nify  a  subject 
only.  '  Whiteness,'  '  lenj^th,'  '  virtue,'  signify  an  attribute 
only.  None  of  the.se  nanv.^s,  therefore,  are  connotativc. 
Hut  'white,'  '  lo.  ■<,'  'virtuous,'  are  connotative.  The 
word  'whit:'  connotes  all  white  things,  as  snow,  paper, 
the  foi  .n  of  the  sea,  etc.,  uid  implies  or,  as  it  was  termed 
by  the  schoolmen,  o  nnoUs  the  attribute  7cliitcucss.  .  .  . 
All  con  Tc*^  general  names  are  connotative.  The  word 
'man,'  for  e.\am|)le,  denotes  Peter,  James,  John,  and  an 
indci  nite  number  of  other  individuals,  of  whom,  taken 
as  a  :lass,  it  is  the  name.  lUit  it  is  applied  to  them 
because  they  possess,  and  to  signify  that  they  ,'os  ss, 
certc'iU  attributes."  ' 

There  is  no  real  ground,  I  think,  for  sur  11.  abso- 
lute distinction  between  connotative  and  n(/n-cunnota- 
tivc  terms.  When  we  consider  the  use  or  rction  of 
terms,  wc  find  that  they  are  never  used  tnerely  to  name 
things,  or  uicir/y  to  connote  attributes,  though  in  cer- 
tain cases  the  former  purj)ose  is  the  primary  one,  and 
in  other  cases  the  latter  object  is  more  prominent. 
Even  when  proper  names  are  employed,  the  qualities  or 
characteristics  of  the  objects  named  are  indirectly  im- 
plied. The  very  fact  that  a  proper  name  is  given  to 
an  object  implies  that  it  possesses  a  certain  definitely 
marked  individuality.  And  a  proper  name  when  used 
intcUii^cntly  carries  with  it  some  still  more  definite  im- 
formation  regarding  the  qualities  of  the  thing  to  which 
it  is  applied,  as,  for  e.xample,  whether  it  is  a  name  of  a 
person,  an  animal,  or  a  place. 

\  »  Mill,  System  of  l.o^ic,  1!U.  i.  Cli.  II.  §  5.    ] 


6o 


TIIK   VAKIOlfS    KINDS   OF  TKKMS 


The    reader    may    consult,    in    connection    with    this 
chapter :  — 

J.  S.  Mill,  Ij\i^h\  Hk.  I.  Ch.  11. 

F.  H.  Hradley,  The  Principles  of  Logic,  pp.  155-173. 

B.  Bosanquet,  Logic,  Vol.  I.,  j)p.  46-71. 

"  "  The  Essentials  of  U^gic,  Lecture  V. 


^ 


H  ' 


this 


ciiaiti:r  V 


DEFINITION    AND    DIVISION 


II 


§  17.  Fixing  the  Meaning  of  Terms.  —  Wc  have  al- 
ready referred  to  the  necessity  of  definitely  fixinf(  the 
meaning  of  the  terms  which  we  employ  in  reasonin*;. 
In  ordinary  life,  words  are  frequently  used  in  a  loose 
and  shifting;  way,  without  any  clear  conception  of  the 
qualities  or  properties  which  they  connote,  or  of  the 
ohjects  to  which  they  apply.  Lo<jjic  demands,  in 
the  first  place,  that_vve_ shall  have  clear  and  definite 
ideas  corresponding  to  our  words,  and  that  the  signifi- 
cation and  scope  of  the  latter  shall  be  carefully  deter- 
mined. But  this  is  a  demand  to  which  little  attention 
is  paid  in  the  ordinary  affairs  of  life.  To  define  our 
terms  in  explicit  language,  or  even  to  make  clear  to 
ourselves  the  ideas  and  things  for  which  they  stand,  is 
by  no  means  a  natural  or  a  universal  mode  of  proced- 
ure, but  something  which  requires  a  distinct,  conscious 
effort. 

Bacon,  Hobbes,  Locke,  Hume,  and  nearly  all  of  the 
older  philosophical  writers  have  warned  us  against  the 
abuse  of  words.  The  whole  matter  has  been  expressed 
very  clearly  by  Locke,  from  whom  I  quote  the  follow- 
ing passage :  — 

'*  For  he  that  should  well  consider  the  errors  and 
obscurity,  the  mistakes  and  confusion,  that  are  spread 

61 


ii*l*<. 


62 


DKIIMIION   AND   DIVISION 


in  the  world  by  an  ill  use  of  words  will  find  sonic 
rciison  to  doubt  whether  lan^ua^c,  as  it  has  boon 
employed,  has  eontril)uted  more  to  the  imi)rovement 
or  hindrance  of  kn{)wled<;e  amonj^st  mankind.  How 
many  are  there,  that  when  they  would  think  on  things 
fix  their  thcnights  only  on  words,  especially  when  they 
would  apply  their  minds  to  moral  matters;  and  who 
then  can  wonder  if  the  result  of  such  contemplations 
and  reasonings,  whilst  the  iileas  they  annex  to  them 
arc  very  confused  and  very  unsteady,  or  perhaps  none 
at  all ;  who  can  wonder,  I  say,  that  such  thoughts  and 
reasonings  end  in  nothing  but  obscurity  and  mistake, 
without  any  clear  judgment  or  knowledge  ? 

"This  inconvenience  in  an  ill  use  of  words  men  suffer 
in  their  own  j)rivatc  meditations  ;  but  much  more 
manifest  are  the  discords  which  follow  from  it  in  con- 
versation, discourse,  and  arguments  with  others.  For 
language  being  the  great  conduit  whereby  men  convey 
their  discoveries,  reasonings,  and  knowledge  from  one 
to  another;  he  that  makes  an  ill  use  of  it,  though  he 
docs  not  corrupt  the  fountains  of  knowledge  which  arc 
in  things  themselves ;  yet  he  does,  as  much  as  in  him 
lies,  break  or  stop  the  pipes  whereby  it  is  distributed  to 
the  public  use  and  advantage  of  mankind."  ^ 

The  remedy  for  the  obscurities  and  confusions  of 
words  is  to  be  found  in  clear  and  distinct  ideas.  We 
must  endeavour  to  go  behind  the  words  and  realize 
clearly  and  distinctly  in  consciou.cness  the  ideas  for 
which    they    stand.      Now  the  means   which   logic  re- 

1  Essay  concerning  Ilutnan  Understanding,  Bk.  III.  Ch.  XI. 


W 


( 


C 


§  18.     UKriNITION 


«3 


sonic 
been 
ment 
I  low 

hinj^s 

they 
I  who 
iitions 

them 
;  none 
ts  unci 
istake, 

I  suffer 

morci 

in  con- 

convey 
)m  one 
luL^h  he 
ich  arc 
in  him 
utecl  to 

tions  of 
IS.     We 

realize 
leas    for 

)gic  re- 

Ixi. 


commends  for  the  attainment  of  this  end  is  defmition. 
The  tirst  rec|uirement  of  logical  reasonin^^  is  that  terms 
shall  be  accurately  detined.  There  are,  however,  two 
ways  in  which  the  meanin;^  of  a  term  may  be  defined 
or  explained.  iCvery  term,  as  we  have  already  seen 
(§  i6),  may  be  re<;arded  either  from  the  point  of  view 
of  intension,  or  from  that  of  extension.  To  define  in 
the  narrower  sense  is  to  explain  from  the  standpoint 
of  intension,  to  state  the  attributes  or  qualities  which 
arc  connoted  by  the  term.  The  process  of  explaining 
terms  with  reference  to  the  objects,  or  classes  of  objects, 
for  which  they  stand  is  known  as  Division.  We  may 
include,  then,  undci'  the  j;eneral  term  definition,  {\)  In- 
tensive dijniition,  or  (icfiiiitioii  in  the  narrower  sense, 
and  (j)  lix tensive  definition  or  division. 

§  1 8.  Definition.  — To  define  a  term  is  to  state  its 
connotation,  or  to  enumerate  the  attributes  which  it 
im])lies.  Thus  we  define  a  parallelogram  as  a  quadri- 
lateral figure  whose  opposite  sides  are  parallel.  A 
distinction  is  often  made  between  verbal  and  real  defi- 
nition. When  we  merely  wish  to  explain  the  mean-j 
ing  in  which  we  intend  to  emi^loy  some  term,  we  have 
verbal  definition.  Hut  when  it  is  the  purpose  of  our 
assertion  to  state  the  real  nature  or  essential  character- 


/ 


istics  ot  some"7)I7ject,_the  proposition  employed  is  said 
to  constitute  a  real  definition.  This  distinction,  though 
not  without  mportance,  cannot,  I  think,  be  regarded  as 
ultimate.  Fur  we  never  define  a  word  or  term  for  its 
own  sake  merely,  but  in  order  to  understand  the  nature 
of  the  objects  to  which  it  refers.     Indeed,  a  mere  word, 


/ 


■fij 


< 


I)i;i'l\HION   AND   DIVISION 


anail  from  the  thintrs  for  which  it  stands,  has  no  inter- 


est for  us.      In    (lefininLf   a  term,  then,   we   are  a 


Iw; 


lyj 


attemptinLC  to  e.\i)Hcate  or  explain,  more  or  less  directly, 
the  nature  of  a  thin<;,  or  our  idea  ahout  a  thing. 

Nevertheless,  there  is  an  advantage  in  distinguishing 
propositions  whose  imuicdiatc  j)urpose  is  to  expound 
the  meaning  of  a  word,  from  those  which  assert  some- 
thing directly  of  an  object.  '  Monarchy  consists  in  the 
authority  of  one  man  over  others,'  may  be  regarded  as  v 
a  \erbal  defmition,  because  the  purpose  of  the  projjo- 
sition  is  simply  to  explain  tiie  meaning  of  the  subject 
term.  On  the  other  hand,  'iron  is  malleable'  is  a  real  ^ 
definition  (though  not  a  complete  one),  because  it  does 
not  j)rimarily  refer  to  the  signification  of  the  word 
'iron,'  but  to  the  real  object  to  which  the  name  is  ap- 
plied. 

In  this  connection,  it  is  interesting  to  notice  that  a  proposition 
which  amounts  to  nothing  more  then  a  verhal  delinition,  is  some- 
times put  forward  as  if  it  were  an  assertion  which  contained  some 
real  knowledge.  The  solemn  commonplaces  in  which  ignorant  ]kt- 
sons  (lelitjht  are  often  of  this  character.  'A  republic  is  a  i^overn- 
ment  by  tlie  people,'  'a  just  man  will  do  what  is  rit^lit,'  "if  it  rains, 
the  ground  will  he  wet,'  may  serve  as  examples.  The  mistake  in 
such  cases  consists  in  supposing  that  these  a.ssertions  arc  anything 
more  than  verhal. 


There  are  two  points  of  view  from  which  the  subject 
of  definition  may  be  consi^^ered.  We  might  either 
discuss  the  best  uietJiod  of  obtninin^i^  real  tlefuiitioiis  of 
tlie  nature  of  tilings,  or  might  confine  our  attentioti  to 
the  requirements  wliieh  a  good  definition  lias  to  fulfil. 
A  person's  ability  to  define   cither  a  ti-rm,  or  the  thing 


•1 


§  i8.     DKIINITION 


f'>5 


/ 


lUcr- 
wLiys 
jctly, 

shing 
)ouncl 
somo- 
n  the 
,cd  as  ^ 
propo- 
ubjcct 
a  /vv?/  / 
t  docs 
:    word 
is  ap- 


)j)()situ)n 
is  sonio- 
cd  s(Hiie 
ant  IHM- 

•l  rains, 
istakr  in 
anything 


subject 
either 

','//.?  of 
ntion  to 
fo  fulfil. 
ic  thing 


I 


lor  whicii  the  term  stands,  depentls,  however,  upon  tiie 
possession  ot  clear  and  chslinct  ideas  on  the  sui)ject. 
The  problem,  then,  as  to  the  best  method  ol  linding 
delinitions,  resolves  itself  into  an  incpiiry  concerning 
the  means  to  be  nsed  in  obtaining  and  classilying  om^ 
ideas  in  general ;  and  the  answer  to  this  (piestion,  so 
far  as  an  answer  can  be  given,  mnst  be  foimd  in  the 
theory  of  logic  as  a  whole.  In  om"  treatment  of  the 
subject  we  shall,  therefore,  confme  our  attention  maiidy 
to  a  consideration  of  the  requirements  of  a  logical 
definition,  and  the  rules  which  nuist  be  observed  in 
stating   it   in   language. 

Hefore  entering  upon  the  sidiji.'ct,  however,  it  is  in- 
teresting to  refer  briefiy  to  the  method  j)roj)osed  by 
Socrates  for  obtaining  defmitions.  Socrates,  as  we 
have  already  seen  (§  5),  was  the  first  to  em|)hasizc 
the  necessity  of  defming  and  fi.ving  the  meaning  of 
familiar  terms,  lie  fotmd  that,  though  the  people  of 
Athens  were  constantly  using  terms  like  'good,'  '  beau- 
tiftd,'  'justice,'  and  'temperance,'  none  of  them,  not 
even  those  with  the  greatest  rei)Utation  for  wisdom,  were 
able  to  give  any  clear  and  consistent  statement  of  what 
these  terms  inij)lied.  Socrate's  himself  did  not  j)rofess 
to  be  wi.ser  than  the  rest,  but  he  had  a  genuine  si)irit 
of  incjuiry,  and  made  it  the  business  of  his  life  to  try  to 
arrive  at  clear  conceptions,  especially  with  regard  to 
certain  fundamental  ethical  virtues,  like  justice,  and 
temperance,  ana  wisdom,  which  he  regarded  as  of  the 
utmost  practical  im])ortance.  It  was  by  means  of  con- 
versation with  others  that  he  sought  to  gain  clear 
ideas    regarding  the    nattire    of   these    virtues.      Hy    a 


„/  J 


k 


GG 


DKKlNirioX    AM)    DIVISION 


M 


i    ! 


scries  of  (jucstions  and  answers,  by  comparison  of 
any  definition  proposed  with  j)articiilar  facts  which  are 
admitted,  he  led  his  interlocutors  to  expose  and  refute 
the  inadequacies  of  their  earher  statements.  In  the 
Republic^  for  example,  the  question  is  re<;"ardin.i;  the 
nature  of  justice.  The  lirst  definition  sui;'^ested  is, 
that  it  is  just  'to  speak  the  truth,  and  to  restore  to 
each  man  his  own.'  Hut  supposin<^  that  a  man  were 
out  of  his  mind  and  demanded  his  weaj^ons  which  had 
been  placed  in  the  hands  of  a  friend,  would  the  friend 
be  an  unjust  man  if  he  refused  to  return  the  \vea{")ons, 
or  abstained  from  tellini;'  the  whole  truth  }  ICvidently 
not.  The  definition  is  then  modified  to  read,  '  It  is  just 
to  {^ive  to  each  man  what  is  his  due.'  Socrates  then 
(juestions  furtlier,  What  is  due  to  each  man  .^  What  is 
due  to  a  friend,  and  what  to  an  enemy  .''  This  leads  to 
the  further  modification  that  'justice  mears  doing  good 
to  our  friends  and  harm  to  our  enemies.'  Hy  referring 
again  to  particular  instances  and  familiar  analogies, 
Socrates  leads  the  person  maintaining  this  definition 
to  admit  that  to  injure  a  person  is  to  make  him  less 
virtuous,  and  therefore  less  just.  But  how  can  justice 
render  the  character  of  another  less  just  than  it  was 
before.''  The  idea  is  absurd;  therefore  the  definition 
has  to  be  abandoned,  and  a  fresh  start  made. 

This  method  of  proceeding  by  means  of  question  and 
answer,  and  thus  compelling  a  speaker  to  admit  par- 
ticiiJar  facts  which  refute  the  general  thesis  which  he 
is  maintaining,  is  called  Dialectic.  This  was  the  means 
by  which  Socrates  constantly  strove  to  advance  to  consis- 
tent and  adetpiate  definitions.     Apart  from  the  dialectical 


I 


ti< 


§  i8.     DEl'IXiriON 


67 


)n    of 
h  are 
•efute 
11   the 
l;    the 
eel   is, 
rire  to 
were 
:h  had 

friend 
apons, 
idently 

is  just 
;s  then 
Vhat  is 
eads  to 

<r    ffood 

lerrinj; 
l()[;ies, 
Inition 
ir.  less 
justice 
it  was 
fuiition 

ion  and 
uit  par- 
hich  he 
means 
consis- 
Lilectical 


and  dramatic  form  which  the  Socratic  ar^auncnt  took, 
the  method  employed  is  essentially  that  of  induction. 
For  the  definition,  or  conception,  is  derived  from  a  com- 
parison of  particular  instances,  both  positive  and  nega- 
tive. By  a  consideration  of  individual  cases,  Socrates 
sought  to  obtain  a  definition  which  would  be  a  complete 
and  adequate  expression  of  the  nature  of  all  the  individ- 
uals which  share  in  the  class  name.  Aristotle  says  that 
it  is  to  Socrates  we  owe  the  method  of  induction  and 
logical  definitions.  Clear  and  distinct  conceptions,  for- 
mulated in  exact  definitions,  constituted  the  scientific 
goal  for  Socrates,  and  the  inductive  procedure  of  ob- 
serving and  classifying  particular  instances  was  the 
means  which  he  emjiloyed  for  reaching  this  goal 

The  second  question  has  reference  to  the  formulation 
of  a  definition  in  language.  Sujiposc  that  we  already 
j)osscss  a  clear  conception  of  the  meaning  of  the  terms 
to  be  defined,  what  are  the  conditions  which  a  logical 
definition  must  fulfil.''  The  answer  to  this  question  is 
usually  given  in  logical  text-books  by  means  of  a  set 
of  rules  for  definition.  Before  stating  these  rules,  how- 
ever, it  is  necessary  to  explain  the  meaning  of  the  terms 
'genus,'  'sjjccics,'  and  'differentia,'  which  will  be  fre- 
quently employed  throughout  the  remainder  of  this 
chapter.  These  terms,  together  with  '  projierty '  and 
'accident,'  constitute  what  the  older  logicians  call  the 
predicables,  and  to  which  a  great  deal  of  importance 
was  supposed  to  belong.  It  will  only  be  necessary, 
however,  for  us  to  consider  briefly  the  signification  of 
the  first  three  terms. 


^ 


m 


(  f\ 


r 


68 


Di:iI>;iTION    AND    UIVlSIiJN 


III  loi^ic,  any  term  may  be  rcf^ardcd  as  a  genus  wliich 
contains  two  or  more  suliordinatc  classes  or  species.v 
A  species,  on  the  other  hand,  is  simi)ly  a  subdivision  or^^ 
subordinate  class  of  some  larger  whole.  Thus  '  metal ' 
is  a  j^enus  with  reference  to  iron,  ^old,  silver,  etc., 
which  are  its  species.  •Rectilinear  fij^ure'  is  the  ^cnus 
to  which  belonj^  the  various  species,  triangle,  cjuadri- 
lateral,  pentagon,  etc.  The  differentia  of  any  term  is 
made  up  of  the  (|ualities  or  characteristics  which  dis- 
tinguish  it  from  other  terms,  from  the  genus  Jo  whicli 
it  belongs,  as  well  as  from  the  species  whi£h  are  co- 
ordinate with  it. __Thus  the  logical  differentia  of  a 
triangle,  is  the  property  of  having  three  sides,  the  dif- 
ferentia of  man,  is  that  whic  h  distinguishes  him  from 
other  animals,  whether  this  be  the  power  of  speech  and 
reason,  or  some  other  characteristic  either  physical  or 
mental. 

The  use  of  the  terms  'genus'  and  'species'  in  logic  is 
entirely  relative.  That  is,  any  term  may  be  considered 
either  as  a  species  or  a  genus,  according  as  it  is  regarded 
as  forming  a  part  of  some  more  comprehensive  class,  or 
as  itself  including  other  classes.  Thus  man,  for  example, 
is  a  species  of  the  genus  '  animal ' ;  bnt  the  same  term 
also  may  be  regarded  as  a  genus  including  various  sjiecies 
of  men,  Caucasians,  Negroes,  Mongolians,  etc.  In  the 
same  way,  '  animal '  may  be  considered  a  species  of  the 
still  more  comprehensive  class  '  organized  being,'  and 
this  latter  term  again  as  a  species  of  the  genus  'material 
being.'  A  still  higher  or  more  comprehensive  term 
'vhich  includes  as  its  species  material  and  spiritual 
be2;i;;s  alii  ^  is  'being.'     Since  this  term  includes  every- 


MOmA^aM^lba 


§  18.     DKFINI  riON 


69 


,'hich  , 
jcics. .' 
on  or^ 
ictiil ' 
etc., 

luidri- 
;rm  is 
h  dis^ 
which, 
.ic  co- 
ol   a 
lie  dif- 
1  from 
:h  and 
ical  or 

)gic  is 
id  e  red 
arded 
iss,  or 
ample, 
le  term 
pecics 
In  the 
of  the 
•  and 
aterial 
e  term 
)iritaal 
cvery- 


S. 


thinpj  which  exists,  and  can  therefore  never  be  incUided 
in  any  more  *  general  class,  it  is  sometimes  called  the 
highest  genus  '  {suu.tnuui  ocims).  On  the  other  hand, 
we  might  proceed  downwards  until  we  come  to  a  class 
which  did  not  adniit  of  division  into  any  subordinate 
classes.  Such  a  term  is  called  in  logic  the  lowest 
species  {injluui  species). 

It  Is  important  to  notice  that  the  terms  'genus  '  ;incl '  species  '  Imve 
not  the  same  sij^nilication  in  io<^ic  as  in  the  natinal  sciences.  In 
classifying  objects  in  natural  history,  we  use  the  terms  '  variety,' 
'species,  'genus,'  'family,'  and  'order.'  (o  denote  varying  degrees  of 
relationship  between  cer'ain  gr()U])s  or  classes  of  objects.  These 
terms,  as  thus  employed,  also  indicate  certain  relatively  fixed  divi- 
sions, or  ])ermanent  ways  of  grouping  the  various  forms  of  jjlant  and 
animal  life.  Hut  \w  logic  the  terms 'genus' and 'sijccies' are  em- 
ployed to  indicate  the  relationship  between  any  higiu-r  and  lower 
class  whatsoever.  Moreover,  as  we  have  seen,  an\  trrm  (excepting 
only  the  highest  genus  and  the  /owesl  sjjccies)  may  be  regarded 
from  ditfcrent  standpoints,  as  either  a  geiuis  or  a  species. 

We  shall  now  i)r()ceed  to  stale  the  requirements  of  a 
logical  definition  :  — 

( I )   A  dijuiitiou  should  state  tJic  essential  attributes     / 
of  the  thiui^  to  be  defuied.     This  is  done  by  stating  the 
genus  to  which  the  object  belongs,  and  also  the  'lecul- 
iar  marks  or  (pialities  by  means  of  which  it  i       istin- 
guished  from  other   memliers  of  the   same  cl;i  Or 

as  the  rule  is  usually  stated :  A  logical  d-tinition 
should  give  the  next  or  jiroximate  genus,  an(  le  dif- 
ferentia of  the  species  to  be  defined.  Thus  define 
a  triangle  as  a  rectilinear  figure  (genus),  having  three 
sides  (differentia);  and  man  as  an  animal  (genus),  which 
has  the  power  of  sjieech  and  reason  (differentia).  ^ 


/    I 


70 


DlUINirioN   AM)    I>I VISION 


■^ 


f 


»r^ 


(2)  ^i   definitio)i  should  not  coutaiti   the    name    to    be 
'dijincd,  nor  any  loord  which  is  directly  synonymous  ivitli 

it.     If,   for  Oaniplc,  \vc  were  to  dofi  ic  justice  as   the 
way  of  actin<^  justly,  or  life  as  the  sum  of   vital    pro-  ' 
cesses,  we  should  be  guilty  of  a  violation  of  this  ruleJ 

(3)  The  dejinition  should  be  exactly  ajuivalent  to  thc\ 
class  of  objects  defined,  that  is,  it  must  be  neither  tool 
broad  nor  too  narnnv.  In  other  words,  the  fletinition 
must  take  account  of  the  whole  class  and  nothing  but 
the  class.  '  A  sensation  is  an  elementary  state  of  con- 
sci(>usness,'  for  example,  is  too  broad  a  definition,  since 
it  applies  equally  to  affective  and  conative  elementary 
processe:;.  On  the  other  hand,  the  defmition  of  gov- 
ernment as  'an  institution  created  by  the  people  for 
the  protection  of  their  lives  and  liberties,'  is  too  nar- 
n>w.  For  it  takes  no  accoiuU  of  absolute  forms  of 
government  which  do  not  depend  upon  the  will  of  the 
people.  Both  of  these  cases  may  be  regarded  as  a 
failure  to  give  !hc  true  differentia  of  the  class  to  be 
defined,  and  hence  as  violations  of  the  first  rule. 

(4)  A  defuition  should  not  be  e.vpressed  in  obscure,  I 
figurative,  or  ambii^uous  lani^uaiy.  The  reasons  for 
this  rule  are  at  once  evident.  Any  lack  of  clearness 
or  definiteness  in  a  definition  renders  it  useless  as  an 
explanation.  So'iietimes  the  words  used  in  defniing 
may  be  less  familiar  than  the  term  to  be  explained 
{ijrnotum  per  i^i^notius).  The  definition  which  was  once 
given  of  the  word  *  net '  as  *a  'cticulated  texture  with 
large  interstices  or  meshes,'  may  serve  as  an  example. 

(5)  /'  definition  should,  whenever  possible,  be  affirma- 
tive rather  than  nci^ative,     A  definition,  that  is,  should 


I 


-:ftj. 


■I 


§  !<;.     DIVfSfON 


71 


the 
as  a 
be 

for 
Lincss 
us  an 
■\ning 
a'Hccl 
s  once 
with 

Ifinna- 
shoukl 


I  • 


state  what  a  term  implies  rather  than  what  it  does  not 
imply.  Sometimes,  however,  the  jiurpose  of  a  defini- 
tion may  be  best  attained  by  a  negative  statement  of 
what  is  excluded  by  the  meaning  of  the  term.  Thus, 
for  example,  we  may  define  a  sj)iritual  being  as  a  being 
wliich  is  not  material,  that  is,  unlike  a  material  body 
made  up  of  parts  extended  in  space. 

A  logical  (li-rinition.  as  has  been  said.  rec|uircs  us  to  mention  the 
proximate  {fiMius  nr  ne.xt  higher  class  to  which  the  species  to  be  defined 
belongs,  and  also  the  .>.pecific  or  characteristic  (htVerences  which  dis- 
tinguish it  from  other  species.  Now  it  is  clear  that  there  are  certain 
cases  in  wliicii  these  conditions  cannot  be  fulfilled.  In  the  first 
phice.  no  logical  definition  can  be  given  of  the  hij^hest  genus,  be- 
cau.sc  there  is  no  more  general  class  to  which  it  can  be  referred. 
And  again,  although  it  is  possible  to  give  the  dilTerentia  of  any 
species  such  as  *  man  '  or  •  metal."  it  is  not  possible  to  state  hidi- 
vidital  characteristics  by  means  of  a  loj^ical  definition.  An  indi- 
vidual thing  may  l)e  perceived,  and  its  various  r.;up.?rtics  pointed 
out.  IJut  it  is  never  possible  to  state  in  a  lo<;ical  .'<  'inition  wherein 
the  individuality  of  a  particular  thing  consists.  The  unic|ueness  of 
a  i)articular  object  cannot  be  summed  up  in  a  general  definition,  but 
must  be  learned  through  perception.  We  may  perhaps  say  that  the 
highest  genus  is  above,  and  the  individual  thing  below,  the  sphere  of 
logical  definition. 

There  are,  nn)reovcr,  other  terms  such  as  *  space.'  'time.''  •life,' 
'thought.'  which  are  not  readily  referred  to  any  higher  class,  and 
for  which  therefore  logical  definitions  cannot  be  given.  These 
terms  are  sometimes  said  to  denote  objixts  which  are  siii  t^cnertSf 
or  of  their  own  class. 

§  19.  Division.  -  \Vc  have  already  .spoken  of  divi- 
sion as  a  process  of  defining  a  term  from  the  point  of 
view  of  extension.  This  is  to  enumerate  the  objects 
or  classes   of  objects   which   the    term    denotes.     This 


72 


DKIINITION    AND    DIVISION 


enumeration  must,  however,  be  ^uitleil  by  eertiiin  i)rin- 
eiples  whieh  we  have  now  to  consider. 

It  is  usual  to  1)e<;in  this  sul)ject  by  speak in^j  of  Di- 
chotomy, or  the  division  of  a  term  into  two  parts  (^<x^ 
refjLi^eiv,  to  cut  in  two).  This  is  a  |)urely  formal  process, 
and  is  based  on  the  so-called  law  of  Excluded  Middle, 
which  is  regarded  as  one  of  the  fundamental  laws  of 
thought.  This  law  may  be  stated  as  follows:  There 
is  no  middle  i^rountl  between  opposites.  Any  term,  (f, 
is  -ither  /;  or  not-/*.  A  triangle  is  either  ecpiilateral  or 
not-ecpiilateral.  Of  two  contradictory  jjredicate.s,  one  or 
the  other  must  belon<;  to  every  possible  subject. 

Now  it  is  clear  that  tiiis  is  a  purely  formal  principle 
of  division.  Some  jjositive  knowledj^e  of  the  particular 
facts  involved  is  always  necessary,  in  order  to  enable 
one  to  determine  what  thin<;s  do  stand  in  this  relation 
of  logical  ()i)position.  The  logical  law,  in  other  words, 
does  not  help  us  at  all  in  deciding  what  may  be  re- 
garded as  not-(i  in  any  particular  case.  It  is  not,  there- 
fore, a  means  of  increasing  our  knowledge,  but  merely 
a  juincipK*  of  order  and  arrangement.  This  fact,  obvi- 
ous as  it  seems,  was  not  understood  by  the  Schoolmen 
who  busied  th'imselves  with  logic  in  the  latter  part  of 
the  Middle  Ages.  They  clung  firmly  to  the  belief  that 
it  was  possible  to  discover  the  nature  of  [)articular  facts 
by  purely  formal  operations  of  this  kind.  Accordingly, 
they  spent  a  great  deal  of  time  in  classifying  and  arrang- 
ing terms  as  contradictions,  contraries,  etc.  This  v.ork 
was  doubtless  of  much  service  in  fixing  the  meaning  of 
terms,  and  in  preventing  confusion  in  their  employment. 
lUit  it  was  ;;  purely  verbal  investigation,   ind  of  course 


m-M 


t 


§  19.     DI  VISION 


73 


could  nf)t  lead  to  any  discoveries  rjyaidiiij;  the  nature 
of  thin<;s. 

Moreover,  it  must  be  noticed  that  wc  do  not  always 
get  propositions  lo  which  any  mean  in  <;  can  be  attached 
by  unitinj;  subjects  and  predicates  in  this  way.  If  the 
law  of  Dichotomy  is  not  guided  by  knowledge  of  the 
particular  facts,  it  will  give  absurd  propositions  like, 
'virtue  is  either  square  or  not-square,'  'iron  is  either 
pious  or  not-pious.'  Unmeaning  propositions  of  this 
kind  being  left  out  of  account,  however,  we  may  proceed 
to  divide  everything  according  to  this  i^rinciple.  All 
geometrical  figures  are  either  rectilinear  or  not-rec- 
tilinear; all  rectilinear  figures  either  triangular  or  not- 
triangular  ;  all  triangles,  ecjuilateral  or  not-ecpiilateral,  etc. 
This  method  of  division  may  be  represented  thus:  — 


% 


Substance 


)e  re- 
he  re- 
erely 
obvi- 
Imen 
lit  of 
f  that 
facts 

ingly, 

lang- 

work 

Ing  of 


Material 


non-material 


I 

Organic 


not-or<^nnic 

J 


mineral 


not-mineral 


gold 


not-gold 


If  it  were  desirable,  the  terms  'non-material,'  'organic,' 
and  *  not-mineral '  might  also  be  further  subdivided  in 
the  same  way. 

Now  it  is  not  difficult  to  see  that  the  practical  use  of 
this  principle  will  dej^end  uj)on  our  ability  to  find  some 
positive  value  for  the  negative  not-d.  That  is,  to  make 
the  law  of  more  than  formal  value,  we  must  know  what 


I   I 


74 


hKKINnioX    AM)    DIVISION 


concrete  term  excludes  n,  or  is  its  loj^ical  contradictory. 
And  knowledf^e  of  this  kind  comes,  as  already  said, 
only  from  experience  of  the  particular  facts.  The 
strictly  loi^ical  opposite  of  a  is  always  not-r? ;  of  wise, 
not-wise,  of  cold,  not-cold,  etc.  Mistakes  fretpiently 
arise  in  statin^^  opposites  in  a  positive  form.  The  diffi- 
culty is  that  terms  arc  chosen  which  are  not  true  logical 
opposites  Thus,  if  we  say  that  every  man  is  either 
wise  or  foolish,  our  terms  are  not  contradictory,  for  a 
middle  ground  between  them  is  {possible.  The  same 
would  be  true  of  divisions  like,  'large  or  small,'  'rich  or 
poor,'  'saint  or  sinner,'  'idle  or  diligent.'  In  general, 
it  is  safe  to  scrutinize  all  dichotomic  divisions  very 
sharply  to  see  that  the  alternatives  are  really  contra- 
dictories. 

The  method  of  dichotomy  depends,  as  we  have  seen, 
upon  the  law  of  Excluded  Middle.  Hut  there  is  also 
another  process  called  Division  in  logic,  which  is  per- 
haps better  known  by  its  less  technical  name  of  Classi- 
fication. In  classification,  there  is  no  necessary  limit 
to  the  number  of  classes  or  divisions  which  may  be  ob- 
tained. In  this  respect,  it  of  course  differs  fundamentally 
from  the  twofold  division  which  we  have  been  exam- 
ining. Fuithermore,  a  classification  is  always  made 
according  to  some  principle  which  is  retained  through- 
out the  whole  process.  Any  common  characteristic  of 
the  grouj)  of  individuals  to  be  divided  may  be  taken  as  a 
principle  of  classification.  If,  however,  the  characteristic 
chosen  is  merely  an  external  and  accidental  one,  the 
classification  based  upon  it  will  be  regarded  as  artificial^ 
and    made    for   some    special    t)r    temporary    purposes. 


I 


§  i<).     hIVISlON 


75 


seen, 
also 
pcr- 
assi- 
imit 
c  ob- 
itally 
xani- 
nracle 

c  of 


^ 


Thus  we  niij^lU  dividi'  all  tlowcriii^j;  plants  uccorilin^'  In 
the  color  of  the  flowers,  or  tlu*  j)ersons  in  any  conij)any 
according  to  the  pattern  of  I  heir  shoes.  A  classification 
which  |)rocee(ls  npon  such  surface  distinctions  has,  of 
course,  no  real  or  scientific  value.  It  does  not  attempt 
to  discover  fundamental  or  deep-lyin^'  resemblances  be- 
tween the  individuals  with  which  it  deals. 

A  scientific  or  natural  classification,  on  the  otiier  hand, 
has  for  its  purpo.se  the  discovery  of  real  likeness  or  resem- 
blance. It  seeks  to  find  and  ^roup  together  the  thin^^s 
which  are  related  in  some  essential  point.  Consequently, 
it  selects  as  its  priiui])le  of  division  some  j)roperty  which 
appears  to  be  a  real  mark  of  individuality,  and  to  be 
connected  with  changes  in  other  proj)erties.  Such  a 
real  principle  t)f  natural  classification  is  rarely  found 
by  comparison  of  merely  one  proj)erty  or  set  of  prop- 
erties in  the  things  to  be  c(»m|)ared.  To  classify  accord- 
ing to  a  single  property  may  be  a  convenient  method 
of  giving  names  to  any  group  of  individuals,  and  of 
arranging  them  in  such  a  way  as  to  be  useful  to  the 
student.  It  does  not,  however,  give  any  adefjuatc  idea 
of  the  properties  and  true  relations  of  the  individuals 
compared.  A  really  scientific,  or  natural,  classification 
must  be  based  upon  a  study  and  comparison  of  all 
the  discoverable  proj^erties  of  the  different  individuals 
to  be  classifieu.  It  is  only  in  this  way  that  their  real 
resemblance  and  affinities  can  be  brought  to  light. 

(I)  The  classification  of  plants  proposed  by  the  famous  Swedish 
liotanist,  Karl  Linnxus  ( 1707  1778),  was  based  upon  the  comparison 
of  a  sins^le  feature  :  the  structuri'  of  the  sexual  or/^ans  of  plants.  Tliis 
method  proved  of  the  greatest  convenience  in  indexing  plants  in  a 


f, 


,/J 


#. 


^. 


Ai 


*'-  ^ 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


I.I 


18 


11.23 


114    IIIIII.6 


Photographic 

Sciences 
Corporation 


// 


m 


w.     ^     /  A  #/^ 


I 


^^•v 


{< 


% 


^ 


'^ 


o 


% 


\ 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  875-4503 


^^ 


'% 


'/,/ 


i^: 


f    m 


:\ 


\i\ 


76 


DEFINITION   AND   DIVISION 


convenient  way  into  genera  and  species  so  tliat  they  could  be  named 
and  described.  Yet  since  the  classification  adopted  was  based  upon 
a  single  property  or  feature  of  the  plant,  it  was  considered  (even  by 
Linnaeus  himself)  as  merely  artificial.  Of  course  it  is  not  so  obvi- 
ously artificial  as  the  examples  of  what  we  may  perhaps  call  merely 
accidental  or  trivial  classification  given  above.  But  Linna;us's 
system  did  not  aim  at  setting  forth  the  true  relations  of  plants,  and  it 
was  not  based  upon  any  systematic  study  of  all  their  properties.  It 
is  useful  merely  as  a  stepping-stone  to  the  real  study  of  plants  which 
is  presupposed  in  natural  classification. 

Certain  rules  for  division  are  usually  given  in  con- 
nection with  the  treatment  of  this  subject.  It  is  not, 
of  course,  supposed  that  by  their  help  one  can  properly 
divide  any  subject  without  special  knowledge.  The 
purpose  of  these  rules  is  rather  to  warn  against  the 
logical  errors  to  which  one  is  most  liable  in  the  process 
of  division. 

(i)  Iwery  division  is  made  on  the  ground  of  differ- 
ences in  some  attribute  (or  attributes)  common  to  all 
the  members  of  the  whole  to  be  divided. 

(2)  Every  division  must  be  based  on  a  single  prin- 
ciple or  ground  {fundamcntum  dhusionis). 

(3)  The  constituent  species  (or  groups  into  which  the 
whole  is  divided)  must  not  overlap,  but  must  be  mutually 
exclusive. 

(4)  The  division  must  be  exhaustive,  i.c.y  the  con- 
stituent species  must  be  equal,  when  added  together, 
to  the  genus. 

The  first  rule  requires  no  remark.  It  simply  states 
that  it  is  only  possible  to  divide  any  whole  on  the  basis 
of  differences  in  something  which  is  common  to  all  its 
parts.     The    second  rule   warns  against  changing  the 


\i 


f  I 


§  i.>     DIVISION 


77 


4 


principle  of  division  while  the  process  is  being  carried 
out.  This  law  would  be  violated,  if,  for  example,  one 
were  to  divide  mankind  into  Caucasians,  Negroes,  Mon- 
golians, Europeans,  Australians,  and  Americans.  The 
principle  of  division  which  was  first  adopted  in  this 
example  was  obviously  that  of  the  color  of  the  skin. 
But  this  principle  was  not  carried  through,  and  another 
principle,  that  of  geographical  distribution,  was  substi- 
tuted for  it.  In  dividing  one  must  be  clearly  conscious 
of  the  principle  which  one  is  using,  and  keep  a  firm 
hold  of  it  until  the  division  is  completed.  The  example 
which  we  have  just  given  also  violates  the  third  rule. 
For  not  all  of  the  groups,  European,  Caucasian,  etc., 
exclude  one  another.  Similarly,  it  would  not  be  good 
logic  to  divide  animals  into  vertebrates,  n^  .mmals,  in- 
sects, birds,  molluscs,  and  fishes.  The  i.ourth  rule 
simjjly  insists  that  the  division  must  be  complete.  The 
whole  must  be  completely  included  in  its  divisions.  It 
would  not  be  a  complete  division  to  say  that  books  may 
be  divided  into  folios^  quartos,  and  duodecimos ;  or 
vertebrates  into  mammals  and  birds.  For  in  neither 
of  these  examples  are  the  divisions  enumerated  equal 
to  the  whole  class. 


■■* 


I. 


v\\ 


"A   .1 


I      » 


References 

J.  S.  Mill,  Logic,  Bk.  I.  Chs.  VII.  and  VIII. 

W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  II.  pp.  82-130. 

C.  Sigwart,  Logic,  Vol.  I.  §§  42-44. 

J.  H.  Hyslop,  The  Elements  of  Logic,  Ch.  VI. 


'\ 


'a. 


;»<iP*' 


0 


CHAPTER   VI 


,    . 


f  ^ 


.; 

! 

|i: 

'(i  \ 

1, 

1'  i 

4 

PROPOSITIONS 

§  20.  The  Nature  of  a  Proposition.  —  A  proposition  is 
the  expression  in  words  of  an  act  of  judgment.  It  is 
composed,  as  we  have  already  seen,  of  two  terms,  a 
subject  and  a  predicate,  connected  by  a  copula.  From 
the  point  of  view  of  formal  logic  the  predicate  is  affirmed 
(or  denied)  of  the  subject.  When  we  come  to  consider 
the  nature  of  judgment  (cf.  especially  §§  74,  yy),  we 
shall  find  reasons  for  questioning  whether  this  analy- 
sis of  the  proposition  can  be  taken  as  furnishing  a  cor- 
rect account  of  what  actually  takes  place  in  judgment. 
When  we  judge,  we  do  not  begin  with  words  or  terms 
which  are  not  yet  judgments,  and  then  pass  on  to  judg- 
ment by  joining  together  the  former  in  an  external  way. 
The  conclusions  which  we  shall  have  to  adopt  are,  _t^hat 
terms  represent  ways  of  judging,  that  the  simplest 
act  of  thought  is  already  a  judgment,  and  that  thinking 
develops  b}''  advancing  from  incomplete  to  more  com- 
plete and  comprehensive  judgments.  The  theory  of 
the  syllogism  is,  however,  worked  out  on  the  view  of 
the  proposition  already  indicated.  This  is  sufficiently 
accurate  for  practical  purposes,  and  is  not  likely  to 
lead  to  any  serious  mistakes  so  long  as  we  remember 
that  it  is  the  proposition,  rather  than  the  actual  nature 
of  judgment,  with  which  we  are  dealing. 

78 


>  .  >\ 


§20.    THE  NATURE   OF  A   PROPOSITION 


79 


ion  IS 
It  is 
ms,  a 
From 
[irmed 
nsider 

7\  we 
analy- 
a  cor- 
yment. 
terms 
)  judg- 
il  way. 
c,  _that 
mplest 
inking 
com- 
ory  of 
iew  of 
ciently 
ely  to 
ember 
nature 


The  logical  proposition,  as  the  expression  of  an  act  of 
thought,  corresponds  to  the  grammatical  sentence.  Not 
every  sentence,  however,  is  a  logical  proposition.  Sen- 
tences which  express  a  wish  or  an  interrogation  do  not 
directly  enter  into  the  process  of  argument  at  all,  and 
may  therefore  be  neglected  for  the  present.  The  same  is 
true  of  exclamatory  sentences.  Again,  even  indicative 
sentences  frequently  require  to  be  rewritten  in  order  to 
reduce  them  to  the  form  of  a  logical  proposition,  which 
demands  two  terms  and  a  copula.  The  sentence,  *  the 
sun  shines,'  must,  therefore,  for  purposes  of  logical 
treatment,  be  reduced  to,  'the  sun  is  a  body  which 
shines.'  '  On  the  hillside  deep  lies  the  snow '  is  ex- 
pressed as  a  logical  proposition  in  some  such  form  as 
this :  *  The  snow  is  a  covering  lying  deep  on  the  hill- 
side.' It  is  very  important  to  change  the  grammatical 
sentence  to  the  regular  form  of  a  proposition  before 
attempting  to  treat  it  logically. 

The  most  general  division  of  propositions  is  that 
which  classifies  them  as  Categorical  and  Conditional.  A 
categorical  proposition  asserts  directly,  and  without  any 
condition.  The  predicate  is  either  affirmed  or  de- 
nied unconditionally  of  the  subject.  *A  is  B,'  'this 
room  is  not  cold,'  '  New  York  is  the  largest  city  in 
America,'  are  examples  of  categorical  propositions. 
Conditional  propositions,  on  the  other  hand,  make  a 
statement  which  is  not  immediately  and  directly  true, 
but  only  claims  to  be  true  under  a  condition ;  as,  e.g., 
*  we  shall  go  to-morrow,  if  it  does  not  rain.'  'It  will 
either  rain  or  snow  to-morrow,'  is  also  a  conditional 
proposition ;  for  neither  rain  nor  snow  are  asserted  di- 


I  ill 

»'■  'Si 


I; 


11" 


'/ 


'  ii 


'I 


f'f 


:  ,i 


I'll 


80 


PROrOSlTIONS 


rectly  and  absolutely,  but  in  each  case  the  appearance 
of  the  one  is  dependent  upon  the  non-appearance  of 
the  other. 

For  the  present  we  shall  deal  only  with  categorical 
propositions,  and  with  the  form  of  syllogistic  argument 
to  which  they  give  rise.  After  we  have  completed  the 
account  of  the  categorical  syllogism,  however,  it  will  be 
necessary  to  return  to  a  consideration  of  conditional 
propositions,  and  the  class  of  arguments  in  which  they 
are  employed.  If 

§  21.   The  Quality  and  Quantity  of  Propositions.  —  We 

shall  now  consider  the  various  kinds  of  categorical 
propositions.  Such  propositions  are  classified  with  re- 
gard to  quality  and  quantity.  From  the  standpoint  of 
quality,  propositions  are  either  affirmative  or  negative. 
An  affirmative  proposition  is  one  in  which  an  agreeirqent 
is  affirmed  between  the  subject  and  predicate,  or  in 
which  the  predicate  is  asserted  of  the  subject.  The 
proposition,  'snow  is  white,'  for  example,  indicates 
such  an  agreement  between  the  subject  and  predicate, 
and  is  therefore  affirmative  in  quality.  A  negathw 
proposition  indicates  a  lack  of  agreement  or  harmony 
between  the  subject  and  predicate.  The  predicate  does^ 
not  belong  to  the  subject,  but  all  relation  or  connection 
between  the  two  is  denied.  *  The  room  is  not  cold,'  'the 
trees  are  not  yet  in  full  leaf,'  are  examples  of  negative 
propositions. 

I  The  quantity  of_a  proposition  is  determined  by  the 
extension  of  the  subject.  When  the  proposition  refers 
to  all  of  the  individuals  denoted  by  the  subject,  it  is  said 


ranee 
ce  of 

orieal 
iment 
;d  the 
rill  be 
itional 
1  they 

--We 

gorical 
nth.  re- 
loint  of 
Bgative. 
cement 

or  in 
The 

dicates 
dicate, 
c  (Til  five 
larmony 
te  does^ 
nection 
d,"the 
egative 

by  the 
In  refers 
It  is  said 


f 


§  21.  THE  QUALITY  AND  QUANHTY  OF  PROI'OSITIONS       8 1 

to  be  universal  in  quantity.  When,  on  the  other  hand, 
the  proposition  affirms  th;U  the. predicate  belongs  only 
to  a  part  of  the  sul)]ect,  it  is  said  to  be  particular.  For 
example,  *  all  metals  are  elements '  is  a  universal  propo- 
sition, because  the  assertion  is  made  of  the  subject  in 
its  widest  or  fullest  extent ;  '  some  metals  are  white '  is 
a  particular  proposition,  because  reference  is  made  to 
only  a  part  of  the  subject  'metal' 

We  divide  propositions,  then,  with  regard  to  quantity, 
^'^it-Gu,JJniv£rsal  and  Particular  propositions.  Universal 
propositions  are  often  indicated  by  adjectives  like  *  al]^' 
'the  whole,'  'every,'  etc.  It  frequently  happens,  how- 
ever, that  no  such  mark  of  universality  is  \>rQ.SQptf^'i\ 
scientific  law  is  usually  stated  without  any  explicit 
statement  of  its  quality,  though  from  its  very  nature  it 
is  meaiat  to  be  universal.  Thus  we  say,  'the  planets 
revolve  arolmd  the  sun,'  'comets  are  subject  to  the  law 
of  gravitation.'  Propositions  which  have  a  singular  or 
an  individual  name  as  subject  are  often  called  Individual 
propositions,  as,  e.g.,  *  the  earth  is  a  planet,'  *  knowledge 
is  power.'  But  since  it  is  impossible  to  limit  a  singular 
subject,  individual  propositions  are  to  be  regarded  as 
universal.     TJiey  belong,  that  is,  to  the  class  of  propo- 


ijions  which  employ  the  subject  term  in  its  complete 


Another  class,  called  Indefinite  or  Indesignate  propo- 
sitions,  has  sometimes  been  proposed.  This  class  is 
ufetially  said  to  include  propositions  in  which  the  form 
of  the  words  does  not  give  any  indication  whether  the 
predicate  is  used  of  the  whole,  or  only  of  a  part  of  the 
subject.     *  Men  are  to  be  trusted,'  *  animals  are  capable 

G 


i. 


1  I'ii 


•■  II 


1 


I  SI 


I 


82 


PRorosnioNs 


of  self-movement,'  may  serve  as  examples.  This  classi- 
fication may  be  useful  in  illustrating;  the  evil  of  making 
indefinite  or  ambiguous  statements.  Otherwise  there 
is  nothing  to  be  learned  from  it.  A  really  indefinite 
proposition  has  no  place  in  an  argument,  and  logic 
rightfully  refuses  to  deal  with  it.  The  first  demand  of 
logic  is  that  our  statements  shall  be  clear  and  precise. 
A  proposition  is  not  necessarily  indefinite,  however, 
because  it  has  no  qualifying  words  like  'all'  or  'some.' 
It  is  t^he  meaning  of  a  proposition  as  a  whole,  rather 
than  the  form  of  its  subject,  which  renders  it  definite 
or  indefinite.  Where,  on  the  other  hand,  it  is  really  im- 
possible to  decide  whether  the  proposition  is  universal 
or  particular,  logic  forbids  us  to  proceed  with  the 
argument  until  this  point  has  been  made  clear. 

Particular  propositions  are  usually  preceded  by  some 
word  or  phrase  which  shows  that  the  subject  is  limited 
in  the  extent  of  its  application.  The  logical  sign  of 
particular  propositions  is  'some,'  but  other  qualifying 
words  and  phrases,  such  as  '  the  greatest  part,'  '  nearly 
all,'  '  several,'  '  a  small  number,'  etc.,  also  indicate  par- 
ticularity. Here  again,  however,  it  is  the  meaning  of 
the  proposition,  rather  than  its  form,  which  is  to  be 
considered.  '  All  metals  are  not  white,'  for  example,  is 
a  particular  proposition,  although  introduced  by  *  all,' 
since  it  is  clearly  equivalent  to  '  some  metals  are  not 
white.'  'Every  mark  of  weakness  is  not  a  disgrace,' 
again,  is  a  particular  proposition,  and  signifies  that  *  not 
all,  or  some  marks  of  weakness  are  not  disgraceful.' 

The  words  *  few '  and  '  a  few '  require  special  atten- 
tion.    The  latter,  as  in  the  proposition,  *  a  few  persons 


K 


V. 


If 


§22.     DIFFICUITIKS    1\   ("I.ASSIKK^VIION 


83 


classi- 
laking 
there 
cfinitc 
logic 
mcl  of 
rccise. 
wever, 
some.' 
rather 
lefinite 
illy  im- 
liversal 
th   the 

y  some 
limited 
sign  of 
ilifying 
nearly 
ite  par- 
ling  of 
to  be 
nple,  is 
*  all; 
are  not 
sgrace,' 
lat  '  not 
ul.' 

1  atten- 
persons 


^ 


V 


\ 


I 


have  spoken  to  me  about  it,'  is  equivalent  to  'some,' 
and  introduces  a  particular  affirmative  ])r()i)()sition. 
'  Few,'  on  the  other  hand,  is  negative  in  character. 
Thus,  'few  were  saved  from  the  shipwreck'  implies  that 
only  a  few  were  saved,  or  that  the  greater  number  did 
not  escape,  and  the  proposition  is  therefore  to  be  con- 
sidered as  a  particular  negative.  lYopositions,  then, 
are  classifiecL.  as__affiniLative  and  negative  in  Quality, 
universal  and  particular  in  Quantity.  When  these  classi- 
fications are  combined,  we  get  four  kinds  of  propositions, 
to  symbolize  which  the  vowels  A,  E,  T,  O  are  employed. 
A  and  I,  the  vowels  contained  in  affiruio,  stand  for 
affirmative  propositions ;  E  and  O,  the  vowels  in  ncgOy 
for  negative  propositions.     This  may  be  represented  as 

follows :  — 

\  Affirmative :  All  S  is  P.  A  "<  e_- 

\  Negative:  No  S  is  P.  '   E. 

^  Affirmative :  Some  S  is  P.  I 


Universal 
Particular 


(    Negative :         Some  S  is  not  P.  ,      O  A 


^ 


We  shall  henceforth  use  A,  E,  I,  and  O  to  represent 
respectively  a  universal  affirmative,  a  universal  negative, 
a  particular  affirmative,  and  a  particular  negative  propo- 
sition. In  dealing  with  propositions  logically,  the  first 
step  is  to  reduce  them  to  one  or  other  of  these  four 
types.  This  can  be  accomplished  readily  by  noticing 
Jthe  distinctions  previously  laid  down.  There  are,  how- 
ever, certain  grammatical  forms  and  sentences  which 
present  some  difficulty,  and  it  may  therefore  be  useful 
to  consider  them  separately. 

§  22.  Difficulties  in  Classification.  —  In  the  first  place, 
we  may  notice   that   in  ordinary    language  the  terms 


\s 


i 


I 


i/Jt-v. 


^- 


'   f 


m  m 


84 


I'uorosrrioNs 


I 


of  a  proposition  arc  frequently  inverted,  or  its  parts 
separated  in  sucli  a  way  that  it  recpiires  attention  to 
determine  its  true  logical  order.  In  tlie  proposition, 
'now  came  still  eveninic  on,'  for  examj^lc,  the  subject 
'still  evening'  stands  between  two  portions  of  the 
predicate.  As  a  logical  proposition,  the  sentence  would 
have  to  be  expressed  in  some  such  form  as  the  follow- 
ing:  'Still  evening  is  the  time  which  now  came  on.' 
Similarly,  we  should  have  to  write  an  inverted  sentence 
like,  'deep  lies  the  snow  on  the  mountain,'  as  'the  snow 
is  something  which  lies  deep  on  the  mountain.' 

If  a  subject  is  qualified  by  a  relative  clause,  the  verb 
of  the  latter  must  not  be  confused  with  the  main  asser- 
tion of  the  proposition.  Take  the  sentence,  '  he  is  brave 
who  conquers  his  passions.'  Here  it  is  evident  that  the 
relative  clause  describes  or  qualifies  'he.'  Logically, 
then,  the  proposition  is  of  the  form  A,  and  is  to  be 
written,  '  he  who  conquers  his  passions  is  brave.'  The 
reader  will  notice  that  all  propositions  which  begin  with 
pronouns  like  'hc-who,'  'whoever,'  etc.,  are  jiru-vcrsal 
ill  quantity,,  since  they  mean  all  who  belong  to  the 
class  in  question. 

(i)  We  have  reduced  grammatical  sentences  to  logical  propo- 
sitions by  changing  the  form  in  such  a  way  as  to  have  two  terms 
united  by  'is'  or  'are'  as  the  copula.  Such  a  proposition,  however, 
does  not  express  time,  but  simply  the  relation  existing  between 
subject  and  predicate.  When  the  grammatical  sentence  does 
involve  a  reference  to  time,  and  especially  to  past  or  future  time, 
the  reduction  to  logical  form  is  somewhat  awkward.  Perhaps  the 
best  method  is  to  t.  row  the  verb  expressing  time  into  the  predi- 
cate. Thus  'the  steamer  will  sail  to-morrow'  =  'the  steamer  is 
a  vessel  which  will  sail  to-morrow ' ;  'we  waited  for  you  two  hours 


U'r] 


or  its  parts 
attention  to 
pro])osition, 

the  sul)jcct 
ons  of  the 
tcnce  would 

the  follovv- 
'  came  on.' 
cd  sentence 
^  '  the  snow 
n.' 

5C,  the  verb 

main  asser- 

hc  is  brave 

nt  that  the 

Logically, 

d  is  to  be 

ive.'     The 

3egin  with 

iiiU-vcrsal 

g  to   the 


ical  propo- 
two  terms 
II,  however, 
g  between 
tence  does 
Jture  time, 
erhaps  the 
the  predi- 
steamer  is 
two  hours 


f 


i 


i 


§23.     RKL.VriON   OF  SUr.JI'X  r   and    I'RKDRATK        85 

yesterday'  =  'we  arc  persons  who  waited  for  you  two  hours  yes- 
terday.' 

(2)  Exclusive  propositions  exclude  all  individuals  or  classes 
cxcci)t  those  mentioned  by  the  use  of  some  such  word  as  '  except,' 
'none  but,'  'only.'  'None  but  the  jj;uilty  fear  the  jud<j;e';  'only 
citizens  can  hold  property';  'no  admittance  except  on  business.' 
These  propositions  may  all  be  reduced  to  the  form  E  by  writing 
'no'  before  the  fiei^ativc  o{  the  subject  term.  Thus  'none  but  the 
guilty  fear  the  judge'  -  '■no  one  who  is  ?ioi  guilty  fears  the  judge'; 
'only  citizens  can  hold  property'  —  ^  no  one  who  is  not  a  citizen, 
etc ' ;  '  no  admittance  except  on  business  "^  —  '■  no  person  who  has  not 
business  is  to  be  admitted.' 

§  23.  Formal  Relation  of  Subject  and  Predicate.  -  We 
have  now  to  consider  how  the  relation  existing  oetween 
the  terms  of  a  proposition  is  to  be  understood.  In  §  16 
it  was  shown  that  every  term  may  be  interpreted  in  two 
ways :  either  from  the  point  of  view  of  extension,  or 
from  that  of  intension.  Extensively,  terms  are  taken 
to  represent  objects  or  classes  of  objects ;  while  their 
meanmg  in  intension  has  reference  to  the  attributes 
or  qualities  of  things.  Now  the  interpretation  of  the 
categorical  proposition  given  by  formal  logic  is  based 
entirely  on  extension.  That  is,  the  subject  and  predi- 
cate are  regarded  as  standing  for  individual  objects 
or  classes  of  objects.  The  question  to  be  considered, 
then,  concerns  the  extensive  relation  of  these  groups  of 
objects  in  the  propositions  A,  E,  I,  and  O. 

This  mode  of  interpreting  propositions  must  not  be 
taken  as  furnishing  an  adequate  theory  of  the  nature  of 
the  act  of  judgment  which  is  expressed  in  the  proposi- 
tion. It  leaves  entirely  out  of  account,  as  we  have 
seen,  the  connection  of  attributes  asserted  by  the  propo- 


\^. 


r^ 


i 


I ; 


1  • 


; 

/; 

m 


PROPOSITIONS 


II 


n 


!  ':     ■', 


sition,  which  in  many  cases  is  the  most  prominent 
part  of  its  sij^nitication.  Thus  the  proposition,  'all 
metals  are  elements,'  implies  that  the  cpiality  of  being 
an  element  is  united  with  the  other  c[ualities  connoted 
by  the  term  '  metal.'  Indeed,  this  interpretation  is 
perhaps  more  natural  than  the  one  given  by  formal 
logic,  namely,  that  the  class  of  metals  is  included  in 
the  class  of  elements.  It  must  be  admitted  that  the 
extensive  way  of  reading  projiositions,  as  affirming  or 
denying  the  inclusion  of  one  class  of  objects  in  another 
class,  frequently  seems  artificial.  Nevertheless,  it  is 
the  view  upon  which  the  historical  account  of  the 
syllogism  is  founded.  And  the  fact  that  this  mode  of 
representing  the  meaning  of  propositions  leads  in 
practice  to  correct  conclusions,  proves  that  it  is  not 
wholly  false.  It  represents,  as  we  have  seen,  one  side 
or  aspect  of  the  meaning  of  propositions. 

From  the  point  of  view  of  formal  logic,  then,  a  logical 
proposition  signifies  that  a  certain  relation  exists  be- 
tween the  class  of  things  denoted  by  the  subject,  and 
that  denoted  by  the  predicate.  This  relation  may  be 
one  of  inclusion  or  of  exclusion.  For  example,  the  prop- 
osition '  all  good  men  are  charitable '  is  interpreted  to 
mean  that  '  good  men '  are  included  in  the  class  of 
'charitable  men.'  On  the  other  hand,  *  no  birds  are 
mammals,'  signifies  that  the  two  classes,  'birds'  and 
*  mammals,'  are  mutually  exclusive.  The  meanings  of 
the  four  logical  propositions  A,  E,  I,  and  O  may  be 
represented  by  means  of  a  series  of  diagrams,  which 
were  first  used  by  the  celebrated  German  mathematician 
Euler,  who  lived  in  the  eighteenth  century. 


[iromincnt 
losition,  '  nil 
ty  of  being 
cs  connoted 
pretiition  is 
1  by  formal 

included  in 
ted  that  the 
[iffirming  or 
ts  in  another 
heless,  it  is 
3unt  of  the 
this  mode  of 
ns  leads  in 
hat  it  is  not 
een,  one  side 

hen,  a  logical 
m  exists  be- 
subjcct,  and 
Ltion  may  be 
dIc,  the  prop- 
ntcrpreted  to 
the  class  of 
no  birds  are 
'  birds '    and 
meanings  of 
d  O  may  be 
grams,  which 
mathematician 


§23.     RKI.ATION   OK  Sl'liJKrr   AND   rRKDICArK        87 

To  represent  the  meaning  of  a  proposition  in  A,  like 
'all  good  men  are  charitable,'  we  draw  a  circle  to  sym- 
bolize the  class  of  charitable  beings,  and  then  place 
inside  it  a  smaller  circle  to  stand  for  men.  The  j^rojio- 
sition,  that  is,  signifies  that  '  good  men '  are  included  in 
the  class  of  'charitable  beings.'  The  subject  belongs 
to,  or  falls  within,  the  larger  class  of  objects  represented 
by  the  predicate. 


n„ 


I''i(;.  I. 

It  must  be  carefully  noted  that  proposition  A  does 
not  usually  assert  anything  0/  tJic  whole  of  its  predicate. 
In  the  example  just  given,  no  assertion  is  made  regard- 
ing the  whole  class  of  'charitable  beings,'  but  only  in  so 
far  as  they  are  identical  with  'good  men.'  There  may 
possibly  be  other  charitable  beings  w^ho  are  not  good 
men,  or  not  men  at  all.  The  meaning  of  the  proposition, 
then,  is  that  '  all  good  men  are  some  charitable  beings.' 
In  other  words,  the  predicate  of  the  ordinary  universal 
affirmative  proposition  is  taken  only  in  a  partial,  or 
limited  extent:  nothing  is  affirmed  of  the  whole  of  the 
circle  of  charitable  beings.  We  denote  this  fact  by 
saying  that  the    predicate    of    proposition  A  is  midis- 


^pJ 


i; 


I? 


Hj 


i      ! 


I     ii 


I        1 


i 


w 


88 


PROrOSITIONS 


tribiited.  The  subject,  on  the  other  hand,  as  a  universal 
term,  is  employed  in  its  fullest  extent,  or  is  distributed. 

In  some  cases,  however,  the  predicate  is  not  a  broader 
term  which  includes  the  subject,  but  the  two  are  equal 
in  extent.  In  the  proposition,  *  all  equilateral  triangles 
are  equiangular,'  for  example,  this  is  the  case.  If  we 
were  to  represent  this  proposition  graphically,  the  circle 
of  equilateral  triangles  would  not  fall  inside  that  of 
equilateral  triangles,  but  would  coincide  with  it.  The 
same  relation  between  subject  and  predicate  holds  in 
the  case  of  logical  definitions.  For  example,  in  the 
definition,  *  monarchy  is  a  form  of  political  government 
where  one  man  is  sovereign,'  the  subject  is  coextensive 
with  the  whole  of  the  predicate.  In  examples  of  this 
kind,  it  is  of  course  obvious  that  the  predicate,  as  well 
as  the  subject,  is  distributed. 

As  an  example  of  proposition  E,  we  may  take  the 
example,  'no  birds  are  mammals.'  The  meaning  of 
this  proposition  is  represented  graphically  by  means 
of  two  circles  falling  outside  each  other  as  in  Fig.  2. 


Fig.  2. 


The  proposition  asserts  that  the  class  of  birds  falls 
completely  without  the  class  of  mammals,  that  the  two 
classes   are   entirely  distinct,   and   mutually   exclusive. 


s  a  universal 
distributed. 
ot  a  broader 
^o  are  equal 
ral  triangles 
case.  If  we 
ly,  the  circle 
side  that  of 
ith  it.  The 
ate  holds  in 
iiple,  in  the 
government 
)  coextensive 
nples  of  this 
icate,  as  well 

lay  take  the 
meaning  of 

y  by  means 
n  Fig.  2. 


f  birds  falls 
:hat  the  two 
y   exclusive. 


§  23.     RELATION   OF  SUBJECT  AND   PREDICATE        89 

iWith  regard  to  quantity,  the  subject  is  of  course  uni- 
versal or  distributed.  And,  in  this  case,  the  predicate  is 
also  distributed.  For  the  proposition  asserts  that  the 
subject  'birds*  does  not  agree  with  any  part  of  'mam- 
mals.' Or,  in  terms  of  the  diagram,  we  deny  that  the 
circle  representing  'birds'  corresponds  with  any  portion 
of  the  circle  'mammals.'  But  to  exclude  the  former  circle 
completely  from  the  circle  which  represents  '  mammals,' 
it  is  necessary  that  we  know  the  whole  extent  of  the 
latter.  Otherwise  we  could  not  be  sure  that  the  sub- 
ject had  not  some  point  in  common  with  it.  Proposition 
E,  therefore,  di.ilnbutes,  or  uses  in  their  widest  extent, 
both  subject  and  predicate. 


Fig.  3. 

The  meaning  of  a  proposition  in  I,  as,  e.g-.,  'some 
birds  are  web-footed,'  is  shown  by  means  of  two  circles 
intersecting  or  overlapping  as  in  Fig.  3.  A  part  of  the 
class  of  birds  corresponds  with  a  part  of  web-footed 
animals.  The  proposition  has  reference  to  the  common 
segment  of  the  two  circles,  which  may  be  large  or  small. 
The  two  circk  •  correspond  in  part  at  least.  In  proposi- 
tion I,  both  subject  and  predicate  are  undistributed.    The 


I  1  ' 


J 


I! 


m 


(Ml 


I 


I  V 


!1 


lit! 


li  i 


90 


PROPOSITIONS 


subject  is,  of  course,  a  particular  or  limited  term.  And, 
as  will  be  clear  from  what  has  already  been  said  in  the 
case  of  jDroposition  A,  reference  is  made  to  only  a 
limited  portion  of  the  predicate.  In  the  example  used, 
the  assertion  refers  only  to  those  A^eb-footed  animals 
which  are  also  birds.  Or  we  may  say  that  the  proposi- 
tion has  reference  only  to  the  common  segment  of  the 
circles  representing  subject  and  predicate.  Nothing  is 
asserted  of  the  other  portions  of  the  two  circles.  In 
other  words,  both  subject  and  predicate  are  employed 
in  a  limited  extent,  or  are  undistributed. 

*  Some  metals  are  not  white,'  may  serve  as  an  example 
of  proposition  O. 


Fig.  4. 

This  proposition  may  be  represented  graphically  as 
in  Fig.  4.  Though  this  is  the  same  form  of  diagram 
as  that  employed  in  the  last  figure,  the  proposition 
refers  now  to  the  outlying  part  of  the  circle  'metals.' 
Some  metals,  it  asserts,  do  not  fall  within  the  sphere  of 
white  substances.  A  larger  or  smaller  section  of  the 
circle  representing  the  former  term,  falls  completely 
without  the  circle  of  white  substances. 


\,T 


;erni.  And, 
1  said  in  the 
i  to  only  a 
:amplc  used, 
ited   animals 

the  proposi- 

mcnt  of  the 

Nothing  is 

circles.  In 
re  employed 

s  an  example 


aphically  as 
of  diagram 
proposition 
le  *  metals.' 
le  sphere  of 
:tion  of  the 
cojnpletcly 


i 


i 


§  23.     RELATION   OF   SUBJECT   AND    PREDICATE        91 

It  is  necessary  to  notice  carefully  that  although  the 
subject  of  O  is  undistributed,  its  predicate  is  distributed. 
For,  as  we  have  seen,  a  part  of  the  subject  is  completely 
excluded  from  the  class  of  'white  substances.'  But  in 
order  to  exclude  from  every  part  of  the  predicate,  the 
full  extent  of  the  predicate  must  be  known.  Or,  in 
terms  of  the  diagram,  the  proposition  excludes  a  portion 
of  the  circle  of  metals  (some  metals)  from  each  and 
every  part  of  the  circle  of  white  things.  The  latter 
term  must  therefore  be  used  in  its  full  extent,  or  be 
distributed. 

It  is  absolutely  necessary,  in  order  to  comprehend 
what  follows,  to  understand  the  distribution  of  terms 
in  the  various  propositions.  It  may  help  the  reader  to 
remember  this  if  we  summarize  our  results  in  the  follow- 
ing way :  — 

Proposition  A,  subject  distribuled,  predicate  und.  .ributed. 
Proposition  E,    subject  distributed,  predicate  distributed. 
Proposition   I,  subject  undistributed,  predicate  undistributed. 
Proposition  O,  subject  undistributed,  predicate  distributed. 

References  to  §  23 

W.  S.  Jevons,  Elementary  Lessons  in  Lo^ic,  pp.  71-75. 

J.  S.  Mill,  Logic,  Bk.  I.  Ch.  V. 

C.  Sigwart,  Logic,  §  5. 

B.  Bosanquet,  The  Essentials  of  Lo^ic,  Lectures  V.  and  VI. 


I 

i 


.,  mil 


I  r: 


■  l\ 


I     » 


\iUv 


CHAPTER   VII 


THE   INTERPRETATION    OF    PROPOSITIONS 


!:;''l 


^ 


§  24.   The  So-called  Process  of  Immediate  Inference. — 

Many  logicians  speak  of  two  kinds,  or  processes  of  reason- 
ing, to  which  they  give  the  names  of  mediate,  and  imme- 
diate inference.  Mediate  inference,  it  is  said,  asserts 
the  agreement  or  disagreement  of  a  subject  and  predi- 
cate after  having  compared  each  with  some  common 
element  or  middle  term.  The  conclusion  is  thus  reached 
mediately  or  indirectly.  The  syllogism  is  the  best 
example  of  mediate  inference.     In  the  syllogism, 

All  M  is  P, 
All  S  is  M, 
Therefore  S  is  P, 

the  conclusion  is  reached  through  the  medium  of  M, 
with  which  both  S  and  P  have  been  compared.  It  will 
be  noticed  that  to  obtain  a  conclusion  in  this  way  two 
propositions  or  premises  are  necessary. 

We  sometimes  are  able,  however,  to  pass  directly 
or  immediately  from  one  proposition  to  another.  For 
example,  the  proposition  that  *no  men  are  infallible,' 
warrants  the  statement  that  '  no  infallible  beings  are 
men.'  Or,  if  we  know  that  it  is  true  that '  some  birds  are 
web-footed,'  we  perceive  at  once  that  the  proposition, 
*  no  birds  are  web-footed,'  is  false.  It  is  this  process  of 
passing  directly  from  one  proposition  to  another  which 
has  been  named  by  many  logicians  immediate  inference. 

92 


r^ 


r 


v^H 


ONS 

Inference.  — 

ies  of  rcason- 
e,  and  imme- 
said,  asserts 
t  and  prcdi- 
nie  common 
;hus  reached 
is  the  best 
logism, 


Hum  of  M, 
ed.  It  will 
lis  way  two 

ss  directly 
)ther.     For 

infallible,' 

beings  are 

^e  birds  are 

roposition, 

process  of 
thcr  which 

inference. 


V   .. 


r^'i 


? 


^ 


§  24.     PROCESS  OF   IMMEDIATE  INFERENCE 


93 


Can  we  be  properly  said  to  infer  at  all  when  we  pass 
from  one  proposition  to  another,  as  in  the  above  ex- 
amples ?  As  we  have  already  shown^  inference  is  a  pro- 
cess of  exhibiting  the  relation  of  facts  to  one  another  bv 
discovering  some  common  element,  or  connecting  prin- 


ciple by jneansjjf  which  they  are  unitedjf'cf.  also  §  8y). 
Wherever  we  can  discover  a  connecting  thread,  or  com- 
mon element  between  two  facts  or  groups  of  facts,  we 
are  able  to  mfcr  with  greater  or  less  certainty  from  the 
nature  of  the  one  what  the  nature  of  the  other  must  be. 
But  it  is  essential  to  inference  that  there  shall  be  a  real 
transition  from  one  fact  to  another  —  that  the  conclu- 
sion reached  shall  be  different  from  the  starting-point. 

The  point  at  issue,  therefore,  is  whether  a  new  fact 
or  truth  is  reached  in  the  so-called  processes  of  imme- 
diate inferences,  or  whether  we  have  the  same  fact 
repeated  in  the  form  of  a  new  proposition.  When  we 
pass  from  *  no  men  are  infallible,'  to  *  no  infallible  beings 
are  men,'  can  we  be  said  to  infer  a  new  truth  ?  In  this 
case  it  is  evident,  I  think,  that  there  has  been  no  real 
development  or  extension  of  the  original  proposition 
so  as  to  include  a  new  fact.  The  new  proposition  is  the 
result  of  a  verbal  interpretation  of  the  original  one,  and 
restates  the  same  fact  in  a  different  way.  Inference 
always  completes  or  enlarges  the  truth  from  which  it 
sets  out  by  showing  the  reasons  which  support  it,  or  the^ 
I  consequences  which  follow  from  it.  But  when  we  pass 
directly  from  one  proposition  to  another,  as  in  the  exam- 
ples given  above,  it  will  be  found,  I  believe,  that  nothing 
I  has  really  been  added  to  the  original  statement — no  new 
I  facts  have  been  brought  into  connection  in  the  process. 


I 


II  iJi" 


!'  '!■ 


*i 


i         ! 


»Vil 


I       » 


V 

»    i 


m 


% 


I 


94 


THE   INrERPRETATION  OF   TROrOSITIONS 


It  is  of  course  true  that  the  claims  of  each  of  the 
different  types  of  so-called  immediate  inference  should 
be  examined  separately.  ]5ut  it  will  be  found,  I  think, 
that  the  conclusion  which  we  have  reached  is  equally 
true  of  all  of  the  forms  to  which  this  name  is  applied. 
It  seems  better  to  regard  these  processes  as  acts  of 
verbal  interpretation,  or  explication  of  the  meaning  of 
propositions,  rather  than  as  inferences  in  the  true  sense 
of  the  word.  They  render  important  service  in  helping 
us  to  understand  what  is  implied  or  involved  in  the 
propositions  ,ve  use,  but  they  do  not  lead  the  mind  on 
to  any  new  truth.  We  may  consider  three  ways  in 
which  propositions  may  be  transformed  as  a  result  of 
the  interpretative  process  —  Opposition,  Obversion,  and 
Conversion. 

§  25.  The  Opposition  of  Propositions.  —  We  have  seen 
that  all  categorical  propositions  have  to  be  reduced  to 
one  of  the  four  forms,  A,  E,  I,  O,  in  order  to  be  dealt 
with  by  logic.  (Now,  when  these  propositions  have  the 
same  subject  and  predicate,  certain  relations  exist  be- 
tween them,  to  which  the  general  name  of  Opposition 
has  been  given.^  It  is  clear  that  the  truth  of  some  of 
these  propositions  interferes  with  the  truth  of  others. 
Thus  if  it  be  true  that  *  no  professional  gamblers  are 
honest,'  it  is  impossible  that  *  all  professional  gamblers 
are  honest,'  or  even  that  some  are  honest.  The  propo- 
sition E  is  thus  inconsistent  with  both  A  and  I.  Again, 
if  it  be  false  that '  all  politicians  are  dishonest,'  it  must  be 
true  that  *  some  politicians  are  not  dishonest,'  though  it 
by  no  means  follows  that  '  no  politicians  are  dishonest.' 


■  j 


[ONS 

each  of  the 
once  should 
ind,  I  think, 
d  is  equally 
!  is  applied. 
1  as  acts  of 
meaning  of 
e  true  sense 
e  in  helping 
Ived  in  the 
he  mind  on 
ee  ways  in 
a  result  of 
version,  and 


;  have  seen 

reduced  to 

to  be  dealt 

IS  have  the 

s  exist  be- 

Opposition 

)f  some  of 

of  others. 

iiblers  are 

I  gamblers 

"he  propo- 

".     Again, 

it  must  be 

though  it 

iishonest.' 


§  25.     THE   OPPOSITION   OF   PROPOSITIONS 


95 


M 


m 


That  is,  when  A  is  false,  O  is  necessarily  true,  while  E 
may  or  may  not  be  true.  Propositions  A  and  E  are 
called  contrary  propositions.  'All  A  is  B,'  and  *no  A 
is  B,'  express  the  greatest  possible  degree  of  contrariety 
or  opposition.  If  one  proposition  be  true,  the  other  is 
necessarily  false.  It  is  to  be  noticed,  however,  that  we 
cannot  conclude  that  if  one  is  false,  the  other  is  true. 
For  both  A  and  E  may  be  false.  Thus,  for  example, 
the  propositions,  *  all  men  are  wise,'  and  *  no  men  are 
wise,'  are  both  false.  But,  on  the  other  hand,  proposi- 
tions A  and  O,  E  and  I,  are  pairs  of  contradictory  prop- 
ositions :  if  one  is  false,  its  contradictory  is  necessarily 
true ;  and  if  one  is  true,  the  other  is  manifestly  false. 

The  relation  of  the  four  logical  propositions  is  clearly 
shown  by  arranging  them  in  the  following  way :  — 

As  Contraries  £      P  Coni- 


\ 

\  0 

/ 

v-^. 

/ 

v^/               y 

' 

E 

\    X 

c 

1. 

y^ 

<o 

73 

/  ^v 

rt 

A 

rf»  y          x 

Q 

3 
CO 

Sub-Contraries 

Fig.  s. 


O' 


? 


i 


\m 


V 


iM 


96 


THE   INTERPRETATION   OF   PROPOSITIONS 


A  and  K  are  known  as  contyarics ;  I  and  O  as  sub- 
contra  n'cs ;  A  and  O,  I  and  E,  as  contradictories ;  A 
and  I,  E  and  O,  arc  subalterns. 

The  relations  of  these  propositions  may  now  be 
summed  up  in  the  following  statements :  — 

(i)  Of  contrary  propositions,  one  is  false  if  the  other 
is  true,  but  both  may  be  false. 

(2)  Of  contradictory  propositions,  one  is  true  and  the 
other  necessarily  false, 

(3)  If  a  universal  proposition  is  true,  the  particular 
which  stands  under  it  is  also  true ;  but  if  the  universal 
is  false,  the  particular  may  or  may  not  be  true. 

(4)  If  a  particular  proposition  is  true,  the  correspond- 
ing universal  may  or  may  not  be  true ;  but  if  the  par- 
ticular is  falcc,  the  universal  must  be  false. 

(5)  Subcontrary  propositions  may  both  be  true;  but 
if  one  is  false,  the  other  is  necessarily  true. 

The  knowledge  that  any  one  of  these  propositions  is 
either  true  or  false  enables  us  to  determine  the  truth  or 
falsity  of  at  least  some  of  the  others. 

For  example,  if  A  is  true,  E  is  false,  O  is  false,  and 
I  is  true.  If  A  is  false,  E  is  doubtful,  O  is  true,  and 
I  doubtful. 

If  I  is  true,  E  is  false,  A  is  doubtful,  and  O  doubtful. 
If  I  is  false,  E  is  true,  A  is  false,  and  O  true. 

Similarly  we  are  also  able  to  determine  what  follows 
when  we  suppose  that  E  and  O  are  either  false  or  true. 

It  ought  to  be  carefully  noted  that  when  we  affirm  the  truth  of 
the  particular  proposition  I,  we  do  not  deny  the  truth  of  the  universal 
proposition  A.  The  proposition,  '  some  students  are  fond  of  recre- 
ation,' for  example,  does  not  exclude  the  truth  of  'all  students  arc 


1 


:ONS 

u\  O  as  sab- 
iictorics ;   A 

lay   now    be 

c  if  the  other 

\  true  and  the 

the  particular 
the  universal 

true. 

le  correspond- 

)ut  if  the  par- 

1  be  true ;  but 

e. 
propositions  is 

ic  the  truth  or 

0  is  false,  and 
O  is  true,  and 

md  O  doubtful. 

true. 

e  what  follows 

er  false  or  true. 

affirm  the  truth  of 
uth  of  the  universal 
i  are  fond  of  recre- 
)f  <all  students  arc 


§25.    THE  orrosiTioN  ov  rK<  )rosiTioNs 


97 


I    I 


1 

^  h  1 


fond  of  recreation.''  Similarly,  the  truth  of  O  does  not  exclude  the 
corresponding  proposition  in  E:  the  statement, 'some  men  are  not 
generous,'  for  example,  does  not  interfere  with  the  truth  ot'  the  uni- 
versal proposition,  '  no  men  are  generous.'  A  particular  proposition, 
in  other  words,  asserts  something  of  a  limited  part  of  a  subject; 
it  neither  affirms  nor  denies  anything  of  the  same  term  taken 
universally. 

The  reader  will  remember  that  propositions  which 
have  the  name  of  some  singular  or  individual  thing  as 
subject,  have  been  classified  as  universal.  *  New  York 
is  the  largest  city  in  Anicrica,'  '  charity  is  not  the  only 
virtue,'  are  examples  of  such  propositions.  Now  it  is  at 
once  evident  that  in  cases  of  this  kind  there  are  no  cor- 
resjoonding  particular  propositions.  What  has  just  been 
said  regarding  the  relation  of  universal  and  particular 
propositions,  applies  therefore  only  to  propositions  which 
have  a  general  term  or  name  as  subject.  Moreover, 
we  must  notice  that  when  A  and  E  propositions  have 
a  singular  or  individual  name  as  subject,  the  relations 
between  them  are  somewhat  different  from  those  just 
stated.  A  and  E,  we  said,  are  contrary,  but  not  contra- 
dictory propositions.  By  that  it  was  implied  that  al- 
though we  can  proceed  from  the  truth  of  the  one  to  the 
falsity  of  the  other,  it  Is  not  possible  to  go  in  a  converse 
direction,  from  falsity  to  truth.  We  cannot  conclude, 
[for  example,  from  the  falsity  of  the  proposition  that 
'  all  men  are  selfish '  the  truth  of  the  corresponding 
1  negative  proposition,  *  no  men  are  selfish.'  With  contra- 
dictory propositions,  however,  we  can  go  from  a  denial 
to  an  affirmation.  Now  the  point  to  be  observed,  with 
regard  to  propositions  with  a  singular  term  as  subject. 


•  .    HH 


■    ( 


I    ' 


l\\XJ 


)\\ 


'ill! 


98 


Tin:  iMKKi'RinA'nox  ok  I'KorusrnoNs 


is  that  although  only  contraries  in  form,  they  liavc  yet 
the  force  of  contradictories.  '  Socrates  is  wise  '  (A), 
and  '  Socrates  is  not  wise  '  (K),  arc  contradictory  as  well 
as  contrary,  i)ropositions. 

§  26.  The  Obversion  of  Propositions.  —  The  terms  '  Ob- 
version  '  and  'ylujuipollence  '  were  formerly  used  to 
denote  any  process  by  which  the  form  of  a  proposition 
is  chanf^ed  without  an  alteration  in  mcanin^^  being 
involved.  The  name  '  Obversion  '  is,  however,  now  gen- 
erally employed  to  describe  the  change  which  a  m^opo- 
sition  undergoes  in  passing  from  the  affirmative  to  the 
negative,  or  from  the  negative  to  the  affirmative  form 
while  still  retaining  its  original  meaning. 

P^very  fact  is  capable  of  expression  either  in  the  form 
of  an  affirmative  or  of  a  negative  proposition.  Whether 
the  affirmative  or  negative  form  is  chosen  in  any  par- 
ticular case,  is  partly  a  matter  of  convenience.  It  is 
also  determined  largely  by  the  psychological  interest  of 
the  moment,  i.e.,  by  the  purpose  which  we  have  in  view 
in  making  the  assertion.  When,  for  example,  we  wish 
to  repel  some  suggestion  which  may  have  occurred  to 
us,  or  to  deny  something  which  our  companions  appear 
to  believe,  we  naturally  choose  the  negative  form  of 
statement.  But  the  meaning  of  the  proposition  is  the 
same  whether  we  say,  'all  men  are  fallible,'  or,  *no  men 
are  infallible.'  Similarly,  we  can  say,  'not  one  of  the 
crew  escaped,'  or,  '  all  of  the  crew  perished.' 

Obversion,  then,  is  the  process  of  substituting  for 
any  affirmative  proposition  its  equivalent  in  negative 
form,  or  of  expressing  the  meaning  of  a  negative  prop- 


I 


IONS 


§26.    TIIK  OliVEKSlON   OV   rROPOSITIONS 


99 


icy  have  yet 
IS  wise '  (A), 
ictory  as  well 


ic  terms  •  Ob- 
erly  used  to 
a  proposition 
leaning  bein^; 
iver,  now  gen- 
^hich  a  m^opo- 
rmative  to  the 
irmative  form 

ler  in  the  form 
;ion.    Whether 
jn  in  any  par- 
snience.     It  is 
;ical  interest  of 
^e  have  in  view 
imple,  we  wish 
ve  occurred  to 
pan  ions  appear 
:rative  form  of 
)position  is  the 
e,'  or,  *  no  men 
not  one  of  the 

ed.' 

iibstituting  for 
mt  in  negative 
,  negative  prop- 


osition as  an  affirmative.  To  obtain  the  obverse  of 
proposition  A,  we  proceed  on  the  principle  that  two 
negatives  are  equal  to  an  affirmative.  Instead  of  'all 
animals  digest  food,'  we  may  write,  '  no  animals  are 
beings^ that  do  not  digest  food';  for,  'every  man  has 
his  own  troubles,'  '  there  arc  no  men  who  have  not 
their  own  troubles.'  Instead  of  affirming  the  predicate 
of  the  subject,  the  obverse  of  A  takes  the  negative  of 
the  original  predicate  and  denies  it  universally. 

Proposition  I  may  be  obverted  in  the  same  way, 
though  it  yields  a  particular,  instead  of  a  universal 
negative  proposition.  Thus  the  obverse  of,  '  some  of 
the  houses  are  comfortable,'  is  *  some  of  the  houses  are 
not  not-comfortable,'  i.e.,  uncomfortable.  We  deny  the 
negative  predicate  in  the  obverse  proposition,  instead  of 
affirming  the  positive. 

We  obtain  the  obverse  of  the  propositions  E  and  O 
by  changing  the  negation  contained  in  them  to  its 
equivalent  affirmation.  This  is  done  by  attaching  the 
negative  to  the  predicate,  and  then  affirming  it  of  the 
subject.  For  example,  to  obtain  the  obverse  of,  *  no  one 
who  was  present  can  forget  the  scene,'  we  first  write  the 
proposition  in  logical  form,  *  no  one  who  was  present  is  a 
person  who  can  forget  the  scene.'  Now  the  negative  of 
the  predicate  term,  *a  person  who  can  forget  the  scene,' 
is,  *a  person  who  can  7wt  forget  the  scene.'  Affirming 
this  universally  we  get,  '  all  persons  who  were  present 
are  persons  who  cannot  forget  the  scene.'  As  an  exam- 
ple of  how  the  obverse  of  O  is  obtained,  we  may  take  the 
proposition,  'some  metals  are  not  white.*  Now  if  we 
change  the  quality  of  the  proposition  by  attaching  the 


I'  J  * 


f  M 


rt    I 


n 


*  \l 


r 

' 

■        ! 

1    ''^ 

1 

i'i 

i 

1    !■■ 

, 

-: 

' 

I 

i;,' 

lOO 


Tm-:  iNTEKriacrATioN  or  PKorosnioNs 


ncfjative  to  the  predicate,  we  obtain  '  some  metals  are  not- 
white.'  That  is,  instead  of  denyin;^,  we  [ifTirm  the  nej;- 
ativc  of  the  orij;inal  predicate.  When  the  predicate  is 
made  up  of  several  words,  it  is  imj^ortant  that  the  logical 
contradictory  of  the  whole  term  be  taken.  For  example, 
in  the  proposition,  'some  men  are  not  fond  of  work,'  the 
predicate  fully  expressed  is,  '  persons  who  are  fond  of 
work.'  Now  the  negative  or  contradictory  term  corre- 
sponding to  this  is,  '  persons  who  are  /lof  fond  of  work.' 
The  obverse  of  the  original  proposition  therefore  is, 
'some  men  are  persons  who  are  not  fond  of  work.' 


^ 


§  27.  The  Conversion  of  Propositions.  —  To  convert  a 
proposition  is  to  transpose  its  subject  and  predicate  so 
that  each  shall  occupy  the  place  previously  held  by  the 
other.  Thus  the  proposition,  '  no  men  are  infallible,'  is 
converted  by  writing  it,  'no  infallible  beings  are  men,' 
The  original  proposition  is  called  the  convertend,  and  the 
proposition  obtained  by  conversion  the  converse.  By 
conversion,  then,  a  new  proposition  is  derived  directly 
from  an  old  one.  It  is  for  this  reason  that  conversion  is 
usually  ranked  as  a  process  of  immediate  inference. 
But,  as  we  have  already  seen,  the  process  of  interpreta- 
tion which  results  in  conversion  seems  to  fall  wholly 
within  the  proposition.  In  other  words,  it  makes  clear 
what  is  involved  in  the  original  proposition,  but  does  not 
lead  to  any  new  fact  with  which  the  latter  is  connected. 
We  therefore  reached  the  conclusion  that  it  might  more 
properly  be  regarded  as  a  process  of  formal  interpreta- 
tion, than  as  one  which  involves  real  inference. 

It  is  evident  that  in  proceeding  to  convert  propositions 


IONS 

ictals  are  not- 
firm  the  neg- 
:  proclicLitc  is 
Kit  the  l()<;leal 
For  example, 
of  work,'  the 
)  are  fond  of 
y  term  corre- 
ond  of  work.' 
therefore  is, 
ji  work.' 

To  convert  a 
1  predicate  so 
[y  held  by  the 
e  infallible,'  is 
ngs  are  men.' 
ertend,  and  the 
converse.  By 
;rived  directly 
t  conversion  is 
ate  inference. 

of  intcrpreta- 

to  fall  wholly 

it  makes  clear 

1,  but  does  not 

is  connected. 

it  might  more 
nal  interpreta- 

rence. 

rt  propositions 


§  27.    THE  CONVERSION  OF   PROPOSITIONS 


lOl 


it  will  be  nccesspry  to  notice  whether  the  predicate  of 
the  convertend,  or  proposition  to  be  converted,  is  dis- 
tributed or  undistributed,  otherwise  we  should  not  know 
what  extension  to  apply  to  this  term  when  used  as 
the  subject  of  the  converse  proposition.  The  rules 
usually  given  to  limit  the  process  of  conversion  are  as 
follows :  — 

(i)  No  term  must  be  distribuied  in  the  converse  prop- 
osition which  was  not  distributed  in  the  convertend. 

(2)   The   quality  of   the   converse    proposition    must 
m       remain  the  same  as  the  quality  of  the  convertend. 

The  reason  for  the  first  rule  is  at  once  evident  from 
what  has  been  already  said.  The  second  rule  is  not  one 
which  is  always  observed.  Of  course,  the  meaning  of 
a  proposition  mu.st  not  be  altered  by  changing  the  qual- 
ity simply  or  directly.  But,  in  converting  by  Contrapo- 
sition, as  we  shall  see  later,  it  is  first  necessary  to  obtain 
the  equivalent  of  the  convertend  by  obversion,  and  this 
necessarily  involves  a  change  of  quality. 

There  are  three  kinds  of  conversion  usually  recog- 
nized :  (n)  Simple  Conversion ;  {d)  Conversion  by  Limi- 
tation QX  per  accidcns;  {c)  Conversion  by  Contraposition. 

{a)  By  Simple  Conversion  is  meant  the  direct  trans- 
position of  the  subject  and  predicate  without  any  other 
change  in  the  form  of  the  proposition.  Both  propositions 
E  and  I  can  be  converted  in  this  way.  Thus  the 
converse  of,  '  none  of  the  books  on  this  shelf  are  novels,' 
is  another  proposition  in  E, '  no  novels  are  books  on  this 
shelf.'  From  *  some  dicotyledons  are  exogens '  we  obtain 
by  conversion  another  particular  affirmative  proposition, 
*  some  exogens  are  dicotyledons.' 


y.il. 


'4.  ■  »>i  iiiminiwii|i  iir 


102 


THE   INTERPRETATION  OF   PROPOSITIONS 


{b)  Conversion  by  Limitation  or  per  accidens  is  applied 
to  proposition  A.  In  this  process  A  loses  its  univer- 
sality, and  yields  as  a  result  only  proposition  I.  To 
illustrate  this  mode  of  conversion  we  may  take  the  propo- 
sition, 'brown  hematite  is  an  iron  ore.'  As  we  already 
know,  the  term  *an  iron  ore,'  being  the  predicate  of 
proposition  A,  is  undistributed.  When  used  as  the  sub- 
ject of  a  new  proposition,  therefore,  it  must  be  limited 
by  the  adjective  'some.'  We  thus  obtain  the  converse 
proposition,  '  some  iron  ore  is  brown  hematite.'  Simi- 
larly, the  converse  of  the  proposition,  '  all  sensations  are 
mental  processes,'  is  *  some  mental  processes  are  sensa- 
tions.' When  proposition  A.is_CQ-QV£rted-bv  limitation, 
then,  it  yields  proposition  I  as  a  result.  And  it  is  evident 
that  the  proposition  has  really  lost  something  in  the 
process.  For  it  is  impossible  by  converting  again  to 
obtain  anything  more  than  a  particular  proposition. 
It  is,  however,  sometimes  possible  to  convert  proposition 
A  without  limiting  the  predicate.  In  formal  definitions, 
for  example,  the  subject  and  the  predicate  are  of  equal 
extent,  and  may  be  transposed  simply  without  any 
limitation  of  the  latter.  Thus  the  converse  of,  *  an 
equilateral  triangle  is  a  plane  figure  having  three  equal 
sides,'  is  *a  plane  figure  having  three  equal  sides  is  an 
equilateral  triangle.' 

{c)  In  Conversion  by  Contraposition  the  negatiye  or 
contradictory  of  the  original  predicate  is  taken  as  the 
subject  of  the  converse  proposition.  This  method  of 
conversion  is  usually  applied  only  to  propositions  A 
and  O. 

When  applied  to  A,  it  means  that  from  a  proposition 


%,.    Hli»".£w^^ 


[ONS 

US  is  applied 
3  its  univer- 
ition  I.  To 
ce  the  propo- 

we  already 
predicate  of 
i  as  the  sub- 
st  be  limited 
the  converse 
itite.'  Simi- 
msations  are 
2s  are  sensa- 
jy  limitation, 
i  it  is  evident 
thing  in  the 
ing  again  to 

proposition, 
t  proposition 
.1  definitions, 
are  of  equal 
without  any 
jrse  of,  '  an 
J  three  equal 
l1  sides  is  an 

negatiye  or 
:aken  as  the 
s  method  of 
^positions  A 


§  27.    THE  CONVERSION  OF   PROPOSITIONS 


103 


in  the  form.  All  B  is  C,  we  are  able  to  assert  something 
of  what  is  not  C.  If  we  know,  for  example,  that  *  all 
the  planets  are  bodies  revolving  around  the  sun,'  we 
can  obtain  by  contraposition  the  proposition,  '  no  bodies 
which  do  not  revolve  around  the  sun  are  planets.'  The 
rule  for  contraposition  is,  first  obvert,  and  then  convert 
simply.  Thus,  the  obverse  of,  'aluminium  is  a  white 
metal,'  is  the  proposition  in  E,  'aluminium  is  not  a 
metal  which  is  not  white ; '  and  converting  this  simply, 
we  get  as  the  contrapositive  of  the  proposition  from 
which  we  started,  '  no  metal  which  is  not  white  is  alu- 
minium.' 

Proposition  O  can  be  converted  only  by  contraposi- 
tion. If  we  were  to  convert  simply,  as,  e.g.,  '  some 
metals  are  not  white,'  *  some  white  things  are  not 
metals,'  we  should  fall  into  error;  for  the  term  'metal' 
is  distributed  in  the  converse  proposition  without  having 
been  distributed  in  the  convertend. 

To  obtain  the  converse  of  O  by  contraposition,  the 
rule  given  above,  first  obvert  and  then  convert  simply, 
applies  once  more.  The  obverse  of  the  proposition  in 
O,  *  some  men  who  make  loud  professions  are  not  to  be 
trusted,'  is  the  equivalent  in  I,  *  some  men  who  make 
loud  professions  are  persons  not  to  be  trusted.'  Con- 
verting this  simply,  we  obtain  the  contrapositive,  *  some 
persons  not  to  be  trusted  are  men  who  make  loud  pro- 
fessions.' 

For  the  sake  of  convenience  we  may  sum  up  the 
treatment  of  Conversion  as  follows :  — 


t-   11; 


'<H 


\     I      • 


L  proposition 


I   i: 


I04 


THE  INTERPRETATION   OF  PROPOSITIONS 


Proposition  A  is  converted  {i)  h  Limit ation^  and  (2)  by  Contra- 
position . 

All  S  is  P.        (A) 
(i)  Converting  by  Limitation,  Some  P  is  S.     (I) 

i.)  Obversion  yields,  No  S  is  ^ 


(2)  Converting  by  Contraposition 


not-P.  (E) 

ii.)  The  Simple  Converse  of  this 
is.  No  not-P  is  S.    (E)     "t 


Proposition  lis  converted  Simply . 
Some  S  is  P.     (I) 
Converting  Simply,  Some  P  is  S.     (I) 

Proposition  E  is  converted  Simply. 

No  S  is  P.     (E) 
Converting  Simply,  No  P  is  S.     (E) 

Proposition  E  may  also  be  converted  by  Contraposition,  but  the 
result  is  the  same  as  the  Contrapositive  of  O.     Thus  for  example :  — 

No  S  is  P.     (E) 

i.)  Obversion  yields,  All  S  is  not- 

P-  (A) 

ii.)  Converting  this  by  Limitation, 

Some  not-P  is  S.      (I) 


Converting  by  Contraposition 


Proposition  O  is  converted  by  Contraposition. 

Some  S  is  not  P.     (O) 

i.)  Obversion  yields.   Some   S  is 

not-P.  (I) 

ii.)  The  Simple   Converse  of  this 
is,  Some  not-P  is  S.     (I) 


Converting  by  Contraposition 


References 

B.  Bosanquet,  Logic ^  Vol.  I.  pp.  310-319. 

W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  IIL  pp.  130-166. 

J.  H.  Hyslop,  The  Elements  of  Logic,  Ch.  X. 


ONS 


(2)  by  Contra- 


\  I 


ields,  No  S  is  ^ 

(E)  \ 

Converse  of  this 


PisS.    (E) 


^ 


CHAPTER  VIII 


THE    SYLLOGISM 


•.    «l 


losition,  but  the 
for  example :  — 

s,  All  S  is  not- 

(A) 
by  Limitation, 

S.      (I) 

is,   Some   S  is 

(I) 

Dnverse  of  this 

P  is  S.     (I) 


.  pp.  130-166. 


§  28.  The  Nature  of  Syllogistic  Reasoning.  —  The  syl- 
logism, as  we  have  already  seen  (§  10),  presents  a  con- 
clusion together  with  the  reasons  by  means  of  which 
it  is  supported.  A  single  proposition  taken  by  itself 
is  dogmatic  :  it  merely  asserts  without  stating  the  grounds 
upon  which  it  rests.  The  syllogism,  on  the  other  hand, 
justifies  its  conclusion  by  showing  the  premises  from 
which  it  has  been  derived.  It  thus  appeals  to  the 
reason  of  all  men,  and  compels  their  assent.  To  do 
this,  it  is  of  course  necessary  that  the  truth  of  the 
premises  to  which  appeal  is  made  should  be  granted. 
If  the  premises  are  disputed  or  doubtful,  the  argument 
is  pushed  a  step  further  back,  and  it  is  first  necessary 
to  show  the  grounds  upon  which  these  premises  rest. 
The  assumption  of  syllogistic  reasoning  —  and,  indeed, 
of  all  reasoning  whatsoever  —  is  that  it  is  possible  to 
reach  propositions  which  every  one  will  accept.  There 
are  certain  facts,  we  say,  well  known  and  established, 
and  these  can  always  be  appealed  to  in  support  of  our 
conclusions.  In  syllogistic  reasoning,  then,  we  exhibit 
the  interdependence  of  propositions ;  i.e,,  we  show  how 
the  truth  of  some  new  proposition,  or  some  proposition 
not  regarded  as  beyond   question,  follows  necessarily 

105 


\'\ 


I  n 


4 ' 


i  i 


il 


ii  I 


1      iKlhj 


\  ^ 


^    ,a 


1 06 


THE  SYLLOGISM 


from  other  propositions  whose  truth  every  one  will 
admit. 

The  question  which  arises  in  connection  with  the 
syllogism,  therefore,  is  this :  Under  what  conaltions 
do  propositions  which  are  accepted  as  true  contain  or 
imply  a  new  proposition  as  a  conclusion  ?  Or  we  may 
put  the  question  in  this  form :  In  what  ways  may  the ' 
four  logical  propositions,  A,  E,  I,  O,  be  combined  so  as 
to  yield  valid  conclusions  ? 

We  pointed  out  in  a  previous  chapter  that  a  syllogism 

has  always  two  premises.     It  is,  however,  impossible  to 

obtain  a  conclusion  by  combining  any  two  propositions 

at  random,  as  e.^:, — 

All  A  is  B. 
No  X  is  Y. 

It  is  evident  that  anj^  two  prop-^sitions  will  not  yield  a 
conclusion  by  being  taken  together.  In  order  to  serve 
as  premises  for  a  syllogism,  propositions  must^  fulfil 
certain  conditions.  <^nd  stand  in  certain  definite  relations 
to  each  other.)  To  determine  some  of  the  most  apparent 
of  these  conditions,  let  us  examine  the  argument :  — 

/Alllniammal^  are  vertebrates, 

*/  The  \vhale  is  a^ammajjj 

J  Therefore  the  whale  is  a  vertebrate. 

It  will  be  noticed  that  the  term  '  mammal '  is  common 
to  both  premises,  and  that  it  does  not  occur  at  all  in  the 
conclusion.  Moreover,  it  is  because  the  other  terms 
are  compared  in  turn  with  this  common  or  Middle  Term 
and  found  to  agree  with  it,  that  they  can  be  united  in 
the  conclusion.  It  is  only  propositions  which  have  a 
middle  term,  therefore,  which  can  be  employed  as  the 


y   one  will 

n  with  the 
conaltions 
contain  or 
Or  we  may 
ys  may  the ' 
bined  so  as 

a  syllogism 
npossible  to 
propositions 


not  yield  a 
der  to  serve 

must_fulfil 
ite  relations 
)st  apparent 
nent : — 


IS  common 
at  all  in  the 
Dther  terms 
MiddleTerm 
e  united  in 
lich  have  a 
Dyed  as  the 


§  28.    THE  NATURE  OF  SYLLOGISTIC   REASONING     107 

premises  of  a  syllogism.  The  syllogism  is  thus  essen- 
tially a  process  of  comparison.  Each  of  the  terms 
entering  into  the  conclusion  is  compared  in  turn  with 
the  same  middle  term,  and  in  this  way  their  relation 
to  each  other  is  determined.  We  reach  the  conclusion 
not  directly  or  immediately,  but  by  means  of  the  middle 
term.  The  conclusion  is  therefore  said  to  be  mediated, 
and  the  process  itself  is  sometimes  called  mediate 
reasoning. 

It  will  be  interesting  to  compare  what  has  just  been  said  regard- 
ing the  function  of  the  middle  term,  with  what  has  been  previously 
stated  regarding  the  nature  of  inference.  When  we  infer  one  fact 
from  another,  it  was  said,  we  do  so  by  discovering  some  identical  link 
or  connecting  thread  which  unites  both.  We  may  say  that  to  infer 
is  to  see  that,  in  virtue  of  some  identical  link  which  our  thought  has 
brought  to  light,  the  two  facts,  or  groups  of  facts,  are  in  a  certain 
sense  identical.  Now  the  middle  term  in  a  syllogism  is  just  the 
explicit  statement  of  the  nature  of  this  identical  link.  It  is  true  that 
in  the  syllogism  we  seem  to  be  operating  with  words  or  terms  rather 
than  with  the  thought-process  itself.  When  we  go  behind  the 
external  connection  of  the  terms,  however,  we  can  see  that  the  middle 
term  represents  the  universal  principle,  by  means  of  which  the  con- 
clusion is  reached.  In  the  example  given  above,  for  instance,  we 
reason  that  the  whale,  being  a  mammal,  is  a  vertebrate. 

The  terms  which  enter  into  the  conclusion  of  a 
syllogism  are  sometimes  called  the  Extremes,  as  opposed 
to  the  middle  term.     Of  the  Extremes,  tJu  predicate  of 

:  tJic  conclusion  is  knozvn  as  the  Major  Term,  and  the  sub- 
ject of  the  conchision  as  the  Minor  Term.     The  premise 

,  which  contains  the  major  term  is  called  the  Major  Premise, 
and  stands  first  when  the  syllogism  is  arranged  in  logical 

]  form.     The  Minor  Premise,  on  the  other  hand,  is  the 


.it 


i«  J 


I 


i         •11 

;    1  ;               iP 

h     1 

1 

11 


!i]  ^.1 


I:)! 


io8 


THE  SYLLOGISM 


premise  which  contains  the  minor  term,  and  stands 
second  in  the  arrangement  of  the  syllogism.  The  prop- 
ositions of  which  the  syllogism  is  composed  may  occur, 
however,  in  any  order  in  actual  reasoning;  either 
premise,  or  even  the  conclusion,  may  stand  first.  To 
arrange  an  argument,  therefore,  it  is  necessary  to 
determine  which  is  the  major,  and  which  the  minor 
premise.  This  can  be  done  only  by  turning  to  the 
conclusion,  and  distinguishing  the  major  and  minor 
terms.     For  example,  take  the  syllogism  :  — 

The  wfiale  suckles  its  young, 
No  fish  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

By  turning  to  the  conclusion  we  see  that  *  fish '  (being 
the  predicate)  is  the  major  term.  The  proposition 
which  contains  this  term,  *no  fish  suckles  its  young,' 
is,  therefore,  the  major  premise,  and  should  stand  first. 
Before  proceeding  to  examine  the  syllogism  further 
it  would  be  necessary  to  arrange  it  as  follows :  — 

No  fish  is  an  animal  which  suckles  its  young, 
The  whale  is  an  animal  which  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

§  29.  The  Rules  of  the  Syllogism.  —  It  is  customary 
to  give  a  number  of  rules  or  canons  to  which  the  syl- 
logism must  conform  in  order  to  yield  valid  conclusions. 
We  shall  first  enumerate  the  rules,  and  afterwards 
remark  on  their  meaning  and  importance. 
^  (i)  In  every  syllogism  there  should  be  three,  and 
only  three,  terms,  and  these  terms  must  be  used 
throughout  in  the  same  sense. 


§  29.    THE   RULES   OF  THE  SYLLOGISM 


109 


and  stands 
.  The  prop- 
;l  may  occur, 
ling ;  either 
id  first.  To 
lecessary  to 
1  the  minor 
rning  to  the 
■   and   minor 


'  fish '  (being 
;  proposition 
s  its  young,' 
d  stand  first, 
^ism  further 
Hows :  — 


'ung, 

is  customary 

hich  the  syl- 

conclusions. 

afterwards 

e   three,  and 
ast    be    used 


The  terms,  as  we  have  already  remarked,  are  known 
as  the  major  term,  the  middle  term,  and  the  minor  term. 

(2)  Every  syllogism  contains  three,  and  only  three, 
propositions. 

These  are  called  the  major  premise,  minor  premise, 
and  conclusion. 

(3)  The  middle  term  must  be  distributed  in  at  least 
one  of  the  premises. 

(4)  No  term  must  be  distributed  in  the  conclusion 
which  was  not  distributed  in  one  of  the  premises. 

(5)  From  negative  premises  nothing  can  be  inferred. 

(6)  If  one  premise  be  negative,  the  conclusion  must 
be  negative ;  and,  conversely,  to  prove  a  negative  con- 
clusion one  of  the  premises  must  be  negative. 

As  a  consequence  of  the  above  rules  there  result  two 
additional  canons  which  may  be  set  down  here. 

(7)  No  conclusion  can  be  drawn  from  two  particular 
premises. 

'  (8)  If  one  of  the  premises  be  particular,  the  conclu- 
sion must  be  particular. 

The  reason  for  the  first  and  second  rules  will  be 
evident  from  what  has  been  already  said  about  the  struct- 
ure of  the  syllogism.  We  saw  that  a  logical  argument 
is  a  process  of  comparison ;  that  two  terms  are  united 
through  comparing  them  with  a  common  or  middle 
term.  If  the  meaning  of  the  terms  does  not  remain 
fixed,  there  are  more  than  three  terms,  and  no  com- 
parison is  possible.  The  second  rule  follows  as  a  corolr 
lary  from  the  first.  ^ 

The  third  rule,  that  the  middle  term  must  be  dis- 
tributed once,  at  least,  is  extremely  important,  and  its 


^ 


(i 


u\ 


111        i 


1 1 


no 


THE  SYLLOGISM 


■'    1 


necessity  will  be  readily  perceived.  For,  since  the 
middle  term  is  the  standard  of  comparison,  it  must  be 
used  in  at  least  one  premise  in  its  universal  extent. 
Otherwise  we  might  compare  the  major  term  with  one 
part  of  it,  and  the  minor  term  with  another  part.  Such 
a  comparison  would  of  course  not  warrant  us  in  either 
affirming  or  denying  the  connection  of  these  terms  in 
the  conclusion.     For  example,  the  two  propositions, 

Sedimentary  rocks  are  stratified  substances, 
Some  metamorphic  rocks  are  stratified  substances, 

do  not  distribute  the  middle  term,  '  stratified  sub- 
stances,* at  all,  being  both  affirmative  propositions.     It 


Fig.  6. 

is  clear  that  the  term,  *  sedimentary  rocks,'  agrees  with 
one  part  of  the  stratified  substances,  and  *  metamorphic 
rocks '  with  another  part.  We  are,  therefore,  not  able 
to  infer  that  *  some  metamorphic  rocks  are  sedimentary 
rocks.'  This  may  be  clearly  shown  by  representing  the 
propositions  by  Euler's  method  of  circles  as  in  Fig.  6. 
We  know  from  the  second  proposition  that  the  circle 
representing  '  metamorphic  rocks '  falls  partly  within  the 


§  29.    THE  RULES  OF  THE   SYLLOGISM 


III 


Hi  I 


or,  since  the 
^n,  it  must  be 
versal  extent. 
:erm  with  one 
r  part.  Such 
t  us  in  either 
hese  terms  in 
)positions, 

h 

Stances, 

stratified  sub- 
•positions.     It 


,*  agrees  with 
'  metamorphic 
fore,  not  able 
i  sedimentary 
)resenting  the 
as  in  Fig.  6. 
lat  the  circle 
tly  wathin  the 


circle  of  'stratified  substances.'  But  it  is  impossible  to 
determine  from  the  statement  whether  it  corresponds  at 
all  with  the  circle  of  sedimentary  rocks,  or  falls,  as  in 
the  figure,  entirely  without  it. 

The  fourth  rule  states  that  no  term  must  be  dis- 
tributed in  the  conclusion  which  was  not  distributed  in 
one  of  the  premises.  That  is,  the  conclusion  must  be 
proved  df  means  of  the  premises,  and  no  term  which 
was  not  employed  in  its  universal  signification  in  the 
premises  can,  therefore,  be  used  universally  or  dis- 
tributively  in  the  conclusion.  This  rule  may  be  violated, 
by  using  either  the  major  or  the  minor  term  in  a  wider 
sense  in  the  conclusion  than  in  the  premise  in  which  it 
occurs.  The  resulting  fallacies  are  then  known  as  the 
Illicit  Process  of  the  major  and  minor  terms  respec- 
tively. As  an  illustration  of  the  illicit  process  of  the 
major  term,  we  may  consider  the  following  argument :  — 

All  rational  beings  are  responsible  for  their  actions, 
Brutes  are  not  rational  beings. 


Therefore  brutes  are  not  responsible  for  their  actions. 

It  will  be  at  once  seen  that  the  major  term,  'beings 
responsible  for  their  actions,'  is  distributed  in  the  con- 
clusion, but  was  not  distributed  when  it  appeared  as  the 
predicate  of  an  affirmative  proposition  in  the  major 
premise.  The  fallacious  nature  of  this  argument  may 
also  be  shown  by  representing  the  proposition  by 
circles. 

The  illicit  process  of  the  minor  term  is  usually  more 
easily  detected.  We  may  take  as  an  example  of  this 
fallacy :  — 


;       i 


\      • 


112 


THE  SYLLOGISM 


i'i 


(  Hi: 


All  good  citizens  arc  ready  to  defend  their  country, 

All  good  citizens  are  persons  who  vote  regularly  at  elections, 

Therefore  all  who  vote  regularly  at  elections  are  ready  to  defend 
tlieir  country. 

It  is  clear  that  the  minor  term,  'persons  who  vote 
regularly  at  elections,'  is  undistributed  when  used  as 
the  predicate  of  the  minor  premise.  In  the  conclusion, 
however,  it  is  wrongly  taken  universally,  and  it  is  this 
unwarranted  extension  to  which  the  name  of  illicit 
minor  is  given.  Students  are  advised  to  draw  circles 
to  illustrate  the  nature  of  this  fallacy. 

The  fifth  and  sixth  rules  have  reference  to  negative 
premises.  It  is  not  difficult  to  understand  why  two 
negative  premises  cannot  yield  any  conclusion.  For, 
from  the  fact  that  S  and  P  are  both  excluded  from  M,  we 
can  conclude  nothing  regarding  their  relation  to  each 
other.  Two  negative  premises  afford  us  no  standard  by 
means  of  which  we  can  determine  anything  concerning 
the  relation  of  major  and  minor  terms.  Again,  where 
one  premise  is  negative  and  the  other  affirmative,  it  is 
asserted  that,  of  the  major  and  minor  terms,  one  agrees, 
and  the  other  does  not  agree,  with  the  middle  term. 
The  necessary  inference  from  these  premises,  then,  is 
that  major  and  minor  terms  do  not  agree  with  each 
other.     That  is,  the  conclusion  must  be  negative. 

It  is  worth  noticing  that  it  is  sometimes  possible  to  obtain  a  con- 
clusion from  premises  which  are  both  negative  in  form.  For  ex- 
ample :  — 

No  one  who  is  not  thoroughly  upright  is  to  be  trusted, 
This  man  is  not  thoroughly  upright, 

Therefore  this  man  is  not  to  be  trusted. 


S2j£!j£eaH»Jt»>»«»»;ll)>« 


2  ready  to  defend 


§  JO.    Tin-:   MdURKS  OK  'rilK   SYI>l,()CiISM 


113 


In  this  example,  altliougli  the  form  of  hotli  premises  is  negative, 
tl'.e  minor  premise  supphes  a  positive  basis  for  argument,  and  is 
really  atlirmative  in  character.  Or  we  may  s.iy  that  the  '  not '  in  the 
predicate  of  the  minor  premise  belon<5s  to  the  predicate,  and  not  to 
tlie  copula.  The  proposition  may  therefore  be  said  to  affirm,  rather 
than  to  deny. 

The  seventh  and  eighth  rules,  which  refer  to  particular  premises, 
can  be  proved  by  considering  separately  all  the  possiijle  cases.  If 
this  is  done,  it  will  be  found  that  these  rules  are  direct  corollaries 
from  the  third  and  fourth,  which  are  concerned  with  the  proper  dis- 
tribution of  terms.  It  is  impossible  to  secure  the  necessary  distri- 
bution with  two  particular  premises ;  for  either  the  distribution  of 
the  middle  term  will  not  be  provided  for.  or  if  this  has  been  secured 
by  means  of  a  negative  premise,  the  conclusion  will  show  a  case  of 
the  illicit  major  term.  By  means  of  the  same  rules,  it  may  be 
shown  that  a  particular  premise  always  requires  a  particular  con- 
clusion. The  truth  of  these  two  subordinate  canons  may  be  also 
readily  shown  by  the  use  of  circles. 


Ml 


i  ^1 " 


I  H 


§  30.  The  Figures  of  the  Syllogism.  —  We  have  seen 
what  an  important  part  the  middle  term  plays  in  the 
syllogism.  It  constitutes  the  mediating  link  between 
the  major  and  minor  terms,  and  makes  possible  their 
union.  Now  upon  the  position  of  the  middle  term  in  the 
premises  depends  the  Figure  of  the  syllogism.  There 
arc  four  possible  arrangements  of  the  middle  term  in 
the  two  premises,  and  therefore  four  figures  of  the 
syllogism.  If  we  let  P  represent  the  major  term,  S  the 
;  minor,  and  M  the  middle  term,  the  form  of  the  different 
[figures  may  be  represented  as  follows  :  — 


First  Figure 
M  — P*' 
S  —  M/ 


Second  Figure 
P  — M^ 
S  — M. 


•.  S  — P 

-^ — ^y 


■.  S  — P 


^ 


i  :!.. 


i 


I  ; 


ili 


,: .' 


114 


lllli  SV1,L()GISM 


Third  riuuRE 
M  -  P 
M  —  S 


I'OURTH   FiriURE 

P  —  M 

M  —  S 


P 


.-.  S  —  P 


In  the  first  figure,  the  middle  term  is  the  subject  of 
the  major  premise,  and  the  predicate  of  the  minor 
premise. 

In  the  second  figure,  the  middle  term  is  predicate  of 
both  major  and  minor  premises. 

The  third  figure  has  the  middle  term  as  the  subject 
of  both  premises. 

In  the  fourth  figure,  the  middle  term  occupies  just  the 
opposite  position  in  the  two  premises  from  that  which 
it  held  in  the  first  figure ;  i.e.,  it  is  the  predicate  of  the 
major  premise,  and  the  subject  of  the  minor  premise. 


:  1 

i 

1 

III. 

i  ■ 

1 

i 

' 

t    '.\' 

i   :i 

,\ 

w 

'■'■' 

■mwi.1  ■■twi 


^  f 


CIIAITKR   IX 

THE   VALID    MOODS    AND    TIIK    REDUCTION   OF    FIGUKES 

§  31.  The  Moods  of  the  Syllogism.  —  By  the  Mood  of 
a  syllogism  we  mean  the  combination  of  propositions 
A,  E,  r,  and  Q.  which  goes  to  make  it  11^  Thus,  when 
a  syllogism  is  made  up  of  three  universal  affirmative 
propositions,  we  speak  of  it  as  the  mood  AAA ;  if  it 
is  composed  of  a  universal  negative,  a  particular  affirma- 
tive, and  a  particular  negative  proposition,  we  name  it 
the  mood  EIO. 

Every  syllogism,  as  has  been  already  .stated,  is  made 

up  of    some    arrangement    of    the    four    propositions 

*A,''E,  1,''0,  taken  three  at  a  time.     Now,  there  are  in 

rail  sixty-four  possible  permutations  of  these  four  propo- 

[sitions  taken  three  at  a  time.      We  might  then  write 

out  these  sixty-four  moods,  and  proceed  to  determine 

[which  of  them  are  valid.     But  this  would  be  a  long  and 

somewhat  tedious  undertaking.      Moreover,  if  we  can 

jdetermine  what  are  the  valid  premises,  we  can  draw  the 

Iproper  conclusions  for  ourselves.      Since,  then,  there 

[are  but  two  premises  in  each  syllogism,  we  shall  have  to 

leal  only  with  the  possible  permutations  of  A,  E,  I,  and  O, 

Uikcn  two  at  a  time,  or  with  sixteen  combinations  in  all. 
The  following,  then,  are  the  only  possible  ways  in 

^hich  the  propositions  A,  E,  I,  and  O  can  be  arranged 

IS  premises :  — 

"5 


'm 


I 


i4 

ii 


'    In 


i  .  "I 


,(   t 


*-uM..jji..'"m 


i .   I 


4 


m 


liN 


!'<         S 


ll6     VALID  MOODS   AND  THE  REDUCTION   OF  FIGURES 


AA" 

EA^ 

lA 

OA 

AE- 

EE^ 

IE' 

OE 

AI^ 

EP 

II 

OI 

AO^ 

EO^ 

lO  - 

00 

Some  of  these  premises,  however,  cannot  yield  concki- 
sions,  since  they  plainly  violate  certain  rules  of  the  syllo- 
gism. The  combinations  of  negative  premises  EK, 
EO,  OE,  and  00  can  be  at  once  struck  out.  Again, 
since  no  conclusion  follows  from  two  particular  prem- 
ises, we  can  eliminate  II,  10,  and  01.  There  remain, 
then,  for  further  consideration  the  combinations :  — 


AA 
AE 
AI 
AO 


EA 


EI 


lA 
IE 


OA 


At  this  point  we  must  recall  the  fact  that  every 
argument  must  belong  to  one  of  the  four  figures.  We 
must  now  therefore  ask  this  question :  Which  of  the 
above  combinations  of  premises  will  yield  valid  con- 
clusions in  the  first,  second,  third,  and  fourth  figures, 
respectively }  By  examining  the  form  of  the  syllogism 
in  each  of  these  figures,  we  shall  be  able  to  discover 
what  conditions  must  be  fulfilled  in  each  case,  and 
to  lay  down  special  canons  for  each  figure.  We  shall 
first  proceed  to  state  and  prove  the  special  canons  of 
the  different  figures.  It  will  not,  however,  be  necessary 
for  the  student  to  commit  these  rules  to  memory,  as  he 
can  always  derive  them  for  himself  by  a  consideration 
of  the  form  of  the  argument  in  the  different  figures. 


'ft: 


3 


OF  FIGURES 


fact   that   every 


§32.    THE  SPECIAL  CANONS  OF  THE   FOUR  FIGURES     II 7 

§  32.  The  Special  Canons  of  the  Four  Figures.  —  ///  tJie 
first  figure y  the  ininor  premise  must  be  affirmative,  and 
the  major  premise  universal. 

The  first  figure  is  of  the  form :  — 

^    M  ^  P^ 

^   S  -^  M*      '    ' 

.-.  S  —  P 

To  show  that  the  minor  premise  is  affirmative,  we 
employ  the  indirect  method  of  proof.  Let  us  suppose 
that  the  minor  premise  is  not  affirmative,  but  negative. 
Then  since  one  premise  is  negative,  the  conchision  must 
be  negative.  But  if  the  conchision  is  a  negative  propo- 
sition, its  predicate,  P,  must  be  distributed.  Any  term 
which  is  distributed  in  the  conchision  must,  however, 
have  been  distributed  when  it  was  used  in  the  premise. 
P  must  be  distributed,  therefore,  as  the  predicate  of  the 
major  premise.  But  since  negative  propositions  alone 
distribute  their  predicates,  the  major  premise,  M  —  P, 
must  be  negative.  But  by  hypothesis  the  minor  prem- 
ise, S  —  M,  is  negative.  We  have,  therefore,  two 
negative  premises,  which  is  impossible.  Our  suppo- 
sition, that  the  minor  premise  is  negative,  is  therefore 
false;  or,  in  other  words,  the  minor  premise  must  be 
affirmative. 

This  having  been  established,  we  can  very  easily 
I  prove  that  the  major  premise  must  be  universal.  For 
the  middle  term,  M,  must  be  distributed  in  at  least  one 
[of  the  premises.  But  it  is  not  distributed  in  the  minor 
[premise,  for  it  is  there  the  predicate  of  an  affirmative 
)roposition.     It  must,  therefore,  be  distributed  as  the 


.'1 


i 


ill 


'r . ' 

i' 


I  :* 


!! 


~?- 


v^ 


'•'      :^'j 


I 


^^sc 


I 

1 

> 

I 

1 

1       i 

1 

1 

1 

3 

i 

1             ! 

i 

!            Mi!' 

i',               ■ 

1             J 

1 

i 

1 

Il8    VALID   MOODS  AND  THE   REDUCTION  OF  FIGURES 

subject  of  the  major  premise,  that  is,  the  major  premise 
must  be  universal. 

If  we  turn  now  to  the  second  figure,  we  shall  find 
that  the  following  rules  may  be  deduced  from  a  con- 
sideration of  its  form  :  — 

(i)  One  premise  must  be  negative ^  and  the  conclusion 
therefore  negative. 

(2)  The  major  premise  must  be  universal. 

The  second  figure  is  in  the  form :  — 

y/  p  ^y  Ml    ^'  '' 

s  ^  ny  ^ 


.'.  S  -^^£v' 
The  reason  for  the  first  rule  is  at  once  evident.  If  one 
premise  is  not  negative,  the  middle  term,  M,  is  not 
distributed,  and  no  conclusion  is  therefore  possible. 
The  only  means  of  securing  distribution  of  the  middle 
term  in  the  second  figure  is  by  means  of  a  negative 
premise.  And  if  one  premise  is  negative,  it  of  course 
follows  that  the  conclusion  must  be  negative. 

This  having  been  established,  the  proof  of  rule  2 
follows  almost  immediately.  For,  since  the  conclusion 
is  negative,  its  predicate,  P,  must  be-distributed.  And 
since  P  is  distributed  in  the  conclusion,  it  must  have 
been  used  distributively  when  it  occurred  as  the  subject 
of  the  major  premise,  or,  in  other  words,  the  major 
premise  must  be  universal. 

The  third  figure  is  of  the  form  :  — 

.  M  ^  P 


M  ^ 


S 


S  -V  P 


tiie  conclusion 


§32.    THE  SPECIAL   CANONS  OF   THE   FOUR  FIGURES     II 9 

From  an  analysis  of  this,  the  two  following  rules  may 
be  obtained :  — 

(i)  TJie  minor  premise  must  be  affirmative. 
(2)  Tlie  conclusion  must  be  particular. 

The  minor  premise  is  here  shown  to  be  affirmative 
by  the  method  employed  ir.  proving  the  same  rule  in 
the  first  figure.  That  is,  we  suppose  the  minor  premise 
negative,  and  show  that,  as  a  result  of  this  hypothesis, 
the  conclusion  is  negative,  and  the  major  term  dis- 
tributed. It  follows,  then,  that  this  term  must  be  dis- 
tributed as  the  predicate  of  the  major  premise.  But 
this  could  happen  only  if  this  premise  were  negative. 
The  hypothesis  that  the  minor  premise  Is  negative  thus 
leads  to  the  absurdity  of  two  negative  premises.  The 
conqkision  that  the  opposite  is  true,  that  the  minor 
premise  is  affirmative,  is  therefore  proved  indirectly. 

Since  the  minor  premise  is  affirmative,  its  predicate 
S  is  undistributed.  This  term  must  therefore  be  used 
in  an  undistributed,  z.^.,  particular  sense  in  the  conclu- 
sion. And,  as  this  term  forms  its  subject,  the  conclu- 
sion is  particular. 

In  the  fourth  figure  the  terms  are  arranged  in  the 

following  way :  — 

P  -  M* 
M  —  S. 


Ji 


'    ^ 


*      '; 


S  -  P 


From  a  consideration  of  the  form  of  this  figure  we  can 
obtain  the  following  special  canons  :  — 

(i)  If  either  premise  be  negative,  the  major  premise 
must  be  universal. 


v'/ 


^Il  '     ftei 


!■■ 


1 20    VALID   MOODS  AND  THE   REDUCFION  OF  FIGURES 

(2)  If  the  major  premise  be  affirmative,  the  minor  must 
be  universal. 

(3)  If  the  minor  premise  be  affirmative,  the  conclusion 
must  be  particular. 

The  student  will  be  able  to  prove  these  canons  for 
himself  by  applying  the  rules  of  the  syllogism  in  the 
same  way  as  has  been  done  in  the  proofs  already  given. 

§  33.  The  Determination  of  the  Valid  Moods  in  Each  of 
the  Figures.  —  We  have  now  to  apply  these  special 
canons  in  order  to  determine  what  moods  are  valid  in 
each  of  the  four  figures.  It  has  already  been  shown 
(p.  116)  that  the  premises  which  are  not  excluded  by 
the  general  rules  of  the  syllogism  are :  — 

A  \  EA  lA  OA 

1.  .  —  IE  — 

AI  EI  —  — 

AO  —  —  — 

Now  we  have  proved  that  in  the  first  figure  the  major 
premise  must  be  universal,  and  the  minor  affirmative. 
The  only  combinations  of  premises  which  will  stand 
these  tests  are,  AA,  EA,  AI,  and  EI.  Drawing  the 
proper  conclusion  in  each  case,  we  have  as  the  four 
valid  moods  of  the  first  figure :  — 

AAA.  FAE,  All,  EIO. 

It  will  be  noticed  that  the  first  figure  enables  us  to 
obtain  as  conclusion  any  one  of  the  four  logical  propo- 
sitions, A,  E,  I,  and  O. 

The  special  canons  of  the  second   figure  state  that 


FIGURES 
minor  tnust 

\e  conclusion 

;  canons  for 
)gism  in  the 
[ready  given. 

ds  in  Each  of 

these   special 

,  are  valid  in 

been  shown 

excluded  by 

3A 


ure  the  major 
or  affirmative, 
ich  will  stand 
Drawing  the 
e  as  the  four 


enables  us  to 
logical  propo- 

<-ure  state  that 


§33.    THE  DETERMINATION  OF  THE   VALID   MOODS     121 

the  major  premise  must  be  universal,  and  one  premise 
negative.  Selecting  the  combinations  of  premises 
which  fulfil  these  conditions,  we  obtain  EA,  AE,  EI, 
and  AO.  These  give,  when  the  conclusion*  have  been 
drawn,  the  following  four  moods  of  the  second  figure  :  — 

EAE,  AEE,  EIO,  AOO. 

By  means  of  the  second  figure,  therefore,  we  are  able 
to  establish  the  truth  only  of  the  negative  propositions, 
r:  and  O. 

In  the  third  figure  the  minor  premise  must  be  affirma- 
tive, and  the  conclusion  particular.  Taking  all  the 
combinations  in  which  the  minor  is  affirmative,  there 
result,  AA,  lA,  AI,  EA,  OA,  EI.  It  must  be  remem- 
bered that  the  third  figure  yields  only  particular  con- 
clusions, even  where  both  premises  are  universal.  The 
valid  moods  in  this  figure  are  therefore  as  follows  :  — 

AAI,  lAI,  All,  EAO,  OAO,  EIO. 

The  canons  of  the  fourth  figure,  which  have  to  do 
with  the  premises,  state  that  where  either  premise  is 
nef,^ative,  a  universal  major  is  necessary,  and  that  an 
affirmative  major  premise  must  be  accompanied  by  a 
universal  minor.  The  combinations  of  propositions 
which  fulfil  these  conditions  are  AA,  AE,  lA,  EA, 
and  EI.  In  drawing  conclusions  from  these  premises, 
however,  it  is  necessary  to  pay  attention  to  the  third 
canon  of  this  figure,  which  states  that  where  the  minor 
premise  is  affirmative,  the  conclusion  must  be  particular. 
Accordingly,  the  valid  moods  of  this  figure  may  now 
be  written :  — 


ii  !'-* 


i  - 


u 


■• 


'    "%  'i 


>.  I 


i     \\  A 


1 

1¥ 

122     VALID   MOODS   AND  THE   REDUCTION   OF   FIGURES 


%V      M 


I  ' 


AAI,  AEE,  lAI,  EAO,  ICIO. 

Here  we  are  able  to  obtain  a  universal  ne<;ative  as  a 
conclusion,  but  not  a  universal  affirmative.  It  is  inter- 
esting to  notice  that  the  first  figure  alone  enables  us 
to  prove  a  proposition  of  the  form  A. 

It  may  also  be  pointed  out  that  the  combination  IE, 
although  not  excluded  by  the  general  rules  of  the  syl- 
logism, cannot  be  used  at  all  as  premises,  since  it  vio- 
lates the  canons  of  all  four  figures.  There  remain  in 
all,  then,  nineteen  valid  moods  of  the  syllogism,  —  four 
in  the  first  figure,  four  in  the  second,  six  in  the  third, 
and  five  in  the  fourth  figure. 


§  34.  The  Mnemonic  Lines.  |— It  is  not  necessary  to 
commit  to  memory  the  valid  moods  in  each  figure.  By 
applying  the  general  rules  of  the  syllogism  to  the  figure 
in  question,  the  student  will  be  able  to  determine  for 
himself  in  every  case  whether  or  not  an  argument  is 
valid.  The  Latin  Schoolmen  in  the  thirteenth  century, 
however,  invented  a  system  of  curious  mnemonic  verses 
for  the  purpose  of  rendering  it  easy  to  remember  the 
valid  moods  in  each  figure.  Although  it  is  not  neces- 
sary for  the  student  to  burden  his  memory  with  these 
barbarous  names,  it  is  interesting  to  understand  the  use 
of  the  lines  :  — 

'     Barbat'a,  Cdcir^nU,  Darii,  Fertoc\n&  prions; 
Cesarc,  Camestres^  Festiiio,  Barohx,  secuadae ; 
Tertia,  Darafti^  Disamis^  Datisi,  Fclapton^ 
Bokardo,  Ferison,  habet;  QuartJi  insuper  acldit 
Braffiantip,  Camenes,  Diinaris,  Fesapo,  Fresison. 

The   words    printea    in    ordinary  type    are   real    Latin 


/ 


FIGURES 


§  34.     Till-:    MNEMONIC   LINES 


123 


irativc  as  a 
It  is  intcr- 
enables  us 

bination  IE, 
s  of  the  syl- 
since  it  vio- 
:e  remain  in 
o-ism,  —  four 
in  the  third, 


necessary  to 
h  figure.     By 
^  to  the  figure 
determine  for 
argument  is 
enth  century, 
emonic  verses 
remember  the 
is  not  neces- 
ry  with  these 
rstand  the  use 


words,  indicating  that  the  four  moods  represented  by 
Barbara,  Cclarent,  Darii,  and  Ferio  are  the  vaHd  moods 
of  the  first  figure,  that  the  next  four  are  vaHd  in  the 
second  figure,  that  the  third  figure  has  six  valid  moods 
represented  by  as  many  artificial  names,  and  that  the 
fourth  figure  adds  five  more.     Each  word  represents  a 
mood,  the  vowels  A,  E,  I,  and  O  indicating  the  quality 
and  quantity  of  the  propositions  which  go  to  compose 
them.     Thus,    Barbara  signifies  the  mood  of  the  first 
figure  which  is  made  un  of  three  universal  affirmative 
propositions    AAA;    Cesare,   a   mood   of   the  second 
figure,    composed    of    the    three    propositions    E  A  E. 
These    lines,    then,    sum    up   the   results    reached    on 
pages  120-22  regarding  the  valid  moods  in  each  figure. 
But  certain  consonants  in  these  mnemonic  words  also 
indicate  how  arguments  in  the  second,  third,  or  fourth 
figures  may  be  changed  to  the  form  of  the  first  figure. 
The   first   figure   was   called   by   A    stotle   the   perfect 
figure,  and  the  second  and   third  the  imperfect  figures, 
since  he  did  not  regard  an  argument  iri  the.  v.    orms  as 
so  direct  and  convincing  as  one  of  the  first-mentioned 
type.     The  fourth  figure  was  not  recognized  by  Aris- 
totle, but  is  said  to  have  been  introduced  into  logic  by 
Galen,  the  celebrated  teacher  of  medicine,  who  lived  in 
the  latter  half  of  the  second  century.     The  process  of 
changing  an  argument  from  one  of  ihe  so-called  imper- 
fect figures  to  that  of  the  first  figure  is  known  as  Reduc- 
tion.    And,  as  we  have  said,  these  curious  but  ingenious 
mnemonic  words  give  rules  for  carrying  out  this  process. 
For  example,  s  indicates  that  the  proposition  represented 
by  the  preceding  vowel  is  to  be  converted  simply.     Thus 


\\ 


i  '    «. 


'    i 


I  j 


./,  P 


^r 


124     VALID    MOODS   AND   THE    REDUCTION   OF   FIGURES 


n 


III 


' 

• :!       . 

\        J 

r,i|            :i| 

an  argument  in  the  second  figure  of  the  mood  Cesare 
is  changed  to  Cclarent  in  the  first  figure,  by  converting 
the  major  premise  simply.  Again,  p  denotes  that  the 
preceding  vowel  is  to  be  converted  by  limitation,  or  per 
accidcHs ;  m  is  supposed  to  stand  for  vintare,  and  indi- 
cates that  the  premises  are  to  be  transposed ;  /•,  which 
is  used  in  the  moods  Baroko  and  Bokardo,  shows  that 
an  indirect  method  of  proof  or  reduction  is  necessary 
to  reduce  the  arguments  to  the  first  figure. 

Further,  the  initial  vowels  of  the  moods  of  the  imper- 
fect figures  correspond  with  those  of  the  moods  in  the 
first  figures,  to  which  they  can  be  reduced.  Cesare  and 
Camestres  of  the  second  figure,  for  example,  and  Ca- 
menes  of  the  fourth  are  reducible  to  Celarent ;  and, 
similarly,  Festino,  Felapton,  Fesapo,  and  Fresison  may 
all  be  reduced  to  Ferio. 

The  student  who  understands  the  structure  of  the  syllogism  will 
be  able  to  arrange  an  argument  in  one  figure  or  another,  as  may  he 
most  convenient,  without  the  aid  of  any  mechanical  rules.  It  mav 
be  interesting,  however,  to  give  a  single  example  for  the  sake  of 
illustrating  the  workings  of  this  most  ingenious  device.  Let  us  take 
the  following  argument  in  the  second  figure  of  the  mood  AEE,  or 
Camestres :  — 


All  members  of  the  class  are  prepared  for  the  examination, 
No  idle  persons  are  prepared  for  the  examination. 

Therefore  no  idle  persons  are  members  of  the  class. 

Now  the  m  in  Camestres  shows  that  the  major  and  minor  premises 
are  to  be  transposed ;  'the  first  ^-  indicates  that  the  minor  premise  is 
to  be  converted,  and  the  second  that  the  same  process  must  be  per- 
formed on  the  conclusion. 

Converting  the  minor  premise  and  transposing,  we  obtain  :  — 


laCURES  ^^ 

:)od  Ccsarc 
converting 
is  that  the 
tion,  or  per 
■e,  and  indi- 
1 ;  k,  which 
shows  that 
s  necessary 

,f  the  imper- 
loods  in  the 
Ccsarc  and 
pie,  and  Ca- 
ilarcnt;  and, 
7resison  may 


le  syllogism  \s'\\\ 
other,  as  may  bo 

rules.  It  may 
;  for  the  sake  of 
CO.     Let  us  take 

mood  AEE,  ov 


§  34.     Till-:   MNEMONIC   LINES 


125 


No  norsons  prepared  for  the  examiuation  are  idle. 
All  members  of  the  class  are  prepared  for  the  examination, 
Converting  the  conchision. 

Therefore  no  memliers  of  the  class  are  idle  persons. 
This  ri'sult.  as  will  at  once  lie  seen,  is  an  argument  in  the  first 
figure  of  tlic  mood  EAE,  or  Celarent. 

References 

Sir  VV.  Hamilton,  Lectures  on  Loi^ic.     Lectures  XX.,  XXL 
A.  Bain,  Logic,  Part  P'irst,  Deduction,  Bk.  II.  Cii.  I. 

Note.  —  It  would  be  interesting  to  work  out,  in  connection  with 
the  various  forms  of  Liductive  reasoning  treated  in  Part  IL,  the 
organic  relation  of  the  syllogistic  Figuresj  and  their  natural  applica- 
bility to  various  purposes  of  argument.  This  task,  however,  seemed 
to  lie  beyond  the  proper  limits  of  this  book.  All  of  the  investiga- 
tions on  tliis  point  start  from  Hegel's  treatment  in  the  second  part 
of  the  Wissenschaft  dcr  Logik  (IVer/ce,  Bd.  5,  pp.  115  fF.).  Those 
interested  in  this  subject  may  consult  W.  T.  Harris,  T/ie  Psychologic 
Foundations  of  Education,  Ch.  IX. -XL,  and  the  same  author's 
Logic  of  Hegel.  See  also  B,  Bosanquet,  Logic,  Vol.  1 1.,  pjD.  44  ff., 
88  if.,  and  The  Essentials  of  Logic,  Lecture  X. 


m\\ 


'  « 


M 


•( 


I  «< 


.  \ 


f  !l 


d  minor  premises 

minor  premise  is 

cess  must  be  per- 

wc  obtain :  — 


1: 


U 


\l' 


•A\  k 


¥ 


'W  I 


CHAPTER   X 


ABBREVIATED    AND    IRREGULAR    FORMS    OF    ARGUMENT 


t  i 


§  35.  Enthymemes.  —  The  term  'enthymeme '  seems  to 
have  been  used  by  Aristotle  for  an  argument  from 
signs  or  from  likelihood,  vvithout  complete  proof. 
From  this  sense  of  logical  incompleteness,  the  name 
has  come  to  be  applied  in  modern  times  to  an  argument 
in  which  some  part  is  omitted.  We  have  already 
noticed,  in  dealing  with  the  syllogism  (§  10),  that  one 
premise  is  often  omitted.  Indeed,  it  is  but  seldom  in 
ordinary  reasoning  that  we  arrange  our  arguments  in 
the  strict  syllogistic  form.  We  hurry  on  from  one  fact 
to  another  in  our  thinking  without  stopping  to  make  all 
the  steps  definite  and  explicit.  We  feel  it  to  be  a  waste 
of  time,  and  a  trial  to  the  patience,  to  express  what  is 
clearly  obvious,  and  so  we  press  on  to  the  conclusion 
which  is,  for  the  time  being,  the  central  point  of  in- 
terest. 

But  the  more  rapid  and  abbreviated  the  reasoning, 
the  more  necessary  is  it  to  keep  a  clear  head,  and  to 
understand  what  conclusion  is  aimed  at,  and  what 
premises  are  assumed  in  the  argument.  To  bring  to 
light  the  hidden  assumption  upon  which  an  argument  is 
based,  is  often  the  best  means  of  refuting  it. 

126 


tl 
tl 


ARGUMENT 

Tie '  seems  to 
ument   from 
plete    proof. 
,s,  the   name 
an  argument 
lave    already 
lo),  that  one 
lUt  seldom  in 
arguments  in 
from  one  fact 
g  to  make  all 
to  be  a  waste 
cpress  what  is 
he  conclusion 
l1  point  of  in- 

tlic  reasoning, 

•  head,  and  to 

at,    and   what 

To  bring  to 

an  argument  is 

it. 


§36.    i;i'Isyll(k;isms  a' <>  i'K(.)SVLiXHiisMs       127 

ICntliymemcs  are  sometimes  naid  to  be  of  the  first, 
second,  or  third  order,  according  as  the  major  premise,, 
the  minor  premise,  or  the  conclusion  is  wanting.  As  a 
matter  of  fact,  an  enthymeme  of  the  third  order  is  a 
rhetorical  device  used  to  call  special  attention  to  a  con- 
clusion which  is  perfectly  obvious,  although  suppressed. 
Thus,  for  example,  *  all  boasters  are  cowards,  and  we 
have  had  proofs  that  A  is  a  boaster.'  Here  the  con- 
clusion is  at  once  obvious,  and  is  even  more  prominent 
than  if  it  were  actually  expressed. 

It  is  usually  easy  to  complete  an  enthymeme.  If  the 
conclusion  and  one  premise  are  given,  the  three  terms 
of  the  syllogism  are  already  expressed.  For  the  con- 
clusion contains  the  major  term  and  the  minor  term ; 
and  one  of  these  again,  in  combination  with  the  middle 
term,  is  found  in  the  given  premise.  From  these  data, 
then,  it  will  not  be  difficult  to  construct  the  suppressed 
premise.  When  the  premises  are  given  without  the 
conclusion,  there  is  no  way  of  determining,  except  from 
the  order,  which  is  major  and  which  is  minor.  It  is 
therefore  necessary  to  assume  that  they  are  already 
arranged  in  proper  logical  order,  and  that  the  subject 
of  the  conclusion,  or  minor  term,  is  to  be  found  in  the 
second  prerhise,  and  the  predicate  of  the  conclusion  or 
minor  premise  in  the  first  premise.  ^.  • 

§  36.  Episyllogisms  and  Prciiyllogisms.  —  In  deductive 
reasoning  it  is  often  necessary  to  carry  on  the  argument 
through  several  syllogisms,  using  the  conclusion  first 
reached  as  a  premise  in  the  following  syllogism.  For 
example,  we  may  argue  :  — 


'.    M't 


'     1 


H 


i 


III  f 


i  J 


li 


\'\ 


11 


128 


.; 


FORMS  OF   AK(;UMFNT 

All  15  is  A  "^ 
All  C  is  n^ 

.-.  All  C  is  A.*' 
But  all  D  is  C 


rr 


/T) 


i. 

1 

n 

1  ! 

i 

.-.  All  D  is  A. 

It  is  clear  that  we  have  here  two  arguments  in  the  first 
figure.  The  first  is  called  the  Episyllogism,  and  the 
latter  the  Prosyllogism.  If  the  argument  were  carried 
on  further,  so  as  to  include  three  or  more  syllogisms,  the 
:!  '■|,,jj  '^^x.  second  would  form  the  Episyllogism  with  respect  to 
.  the  third,  while  the  third  would  be  the  Prosyliogism  of 
the  second.  A  concrete  example  of  this  kind  of  reason- 
ing may  now  be  given  :  — 

All  timid  men  are  suspicious, 
All  superstitious  men  are  timid, 

Therefore  all  superstitious  men  are  suspicious. 
But  some  educated  men  are  superstitious, 

Therefore  some  educated  men  are  suspicious. 

It  will  be  noticed  that  in  these  examples  the  argument  advances 
from  the  premises  of  the  Episyllogism,  to  the  conclusion  of  the  Pro- 
syllogism.  It  proceeds,  that  is  to  say,  in  a  forward  direction,  de- 
veloping the  consequences  of  the  premises  which  form  its  startinj,'- 
point.  This  mode  of  investigation  is  therefore  called  the  Progres- 
sive or  Synthetic,  since  it  goes  steadily  forward  building  up  its  results 
as  it  advances.  To  state  the  same  thing  in  different  words,  we  may 
say  that  the  Progressive  or  Synthetic  method  advances  from  the 
conditions  to  what  is  conditioned,  from  causes  to  effects. 

But  it  is  often  necessary  to  proceed  in  the  opposite  way.  We 
have  often  to  go  back  and  show  the  grounds  upon  which  our  prem- 
ises rest,  instead  of  going  forward  to  show  what  consequences 
follow  from  them.  And  when  we  do  this  we  proceed  Regressii'cly 
or  Analytically .  To  take  an  example  which  will  illustrate  both 
ways  of  proceeding :  — 


■::'^. 


§J7-    SOKITKS,  OK  CHAINS  OK   kEASONING         1 29 

No  man  is  infallihlt'.  for  no  man  is  omniscient, 
Aristotle  was  a  man, 


Therefore  Aristotle  was  not  infallible. 
Ill  advancing  from  the  premises  to  the  conclusion  in  this  argument 
our  procedure  is  progressive  or  synthetic.  Instead  of  reasoning  out 
the  consequences  of  the  premises,  however,  we  may  go  hack  and 
sliow  the  grounds  upon  which  the  major  premise  rests.  It  is  evident 
that  this  premise  is  itself  the  conclusion  of  a  syllogism  which  may 
be  ex[)ressed  as  follows  :  — 

All  infallible  beings  are  omniscient, 

No  man  is  omniscient,  - 

Therefore  no  man  is  infallible. 
The  regressive  method  goes  backward  from  conclusions  to  premises, 
or  from  the  conditioned  to  its  necessary  conditions.     In  scientific 
investigation  it  reasons  from  effects  to  causes,  while  the  synthetic 
nic'thod  advances  from  causes  to  effects. 

§  37.  Sorites,  or  Chains  of  Reasoiing.  —  A  Sorites  is 
an  abbreviated  form  of  syllogistic  reasoning  in  which 
a  subject  and  predicate  arc  united  by  means  of  several 
intermediate  terms.  Such  a  train  of  reasoning  repre- 
sents several  acts  of  comparison,  and  therefore  several 
syllogistic  steps.  But  instead  of  stopping  to  draw  the 
conclusion  at  each  stage,  the  sorites  continues  the 
processes  of  comparison,  and  only  sums  up  its  results 
at  the  close.  We  may  define  the  sorites,  therefore,  as 
a  scries  of  episyllogisms  and  prosyllogisms  in  which  all 
of  the  conclusions,  except  the  last,  are  suppressed.  It 
is  usually  stated  in  the  following  form :  — 

All  A  is  B 
All  B  is  C 
All  C  is  D 

All  D  is  E  * 

.*.    All  A  is  E. 


•I 


i 


I  1 


'9  ^^^HK' 


I'"^* 


r 


■Mfcnaam*. 


130 


FORMS  OK  ARGUMENT 


iri 


',1  ' 

lil.         ..L 

It  is  evident  that  this  train  of  reasoning  fully  expressed 
is  equivalent  to  the  following  three  syllogisms  ;  — 


First  Syllogism 
All  B  is  C 
All  A  is  B 


All  A  is  C  (I). 


Second  Syllogism 
All  C  is  D 
All  A  is  C  (I) 

.-.  All  A  is  D  (2). 


Third  Syllogism 
All  D  is  E 
All  A  is  D  (2) 

•.  All  A  is  E  (3). 


There  are  two  rules  to  be  observed  in  using  this  form 
of  the  sorites  :  (i )  The  first  premise  may  be  particular,  all 
the  others  must  be  universal ;  (2)  the  last  premise  may 
be  negative,  all  the  others  must  be  affirmative.  It  is 
evident  from  an  examination  of  the  syllogisms  given 
above  that  if  any  premise  except  the  first  were  partic- 
ular, the  fallacy  of  undistributed  middle  would  be  com- 
mitted. For,  in  that  case,  the  middle  term  in  one  of  the 
syllogisms  would  be  the  subject  of  a  particular  propo- 
sition, and  the  predicate  of  an  affirmative  proposition. 
And  if  any  premise  but  the  last  were  negative,  the 
major  term  in  the  syllogism  in  which  this  occurred 
would  be  distributed  in  the  conclusion  without  having 
been  distributed  in  the  major  premise.  We  may  now 
give  some  concrete  examples  of  this  kind  of  reason- 
ing:— 

Misfortunes  sometimes  are  circumstances  tending  to  improve 
the  character. 

Circumstances  tending  to  improve  the  character  are  promoters 
of  happiness, 

What  promotes  happiness  is  good, 

Therefore  misfortunes  are  sometimes  good. 

In  some  cases  the  different  terms  of  an  argument  of 
this   kind   are  expressed  in  the  form  of   hypothetical 


,11  A  is  E  (3). 


ing  to  improve 


:r  are  promoters 


argfument  of 


•\     •«      •    - 
§  37.     iiORirES,   OR  CHAINS   OF   REASONING 


131 


propositions.  Thus,  for  example,  we  nii<,ht  argue:  If 
a  man  is  avaricious,  he  desires  more  than  he  possesses ; 
if  he  desires  more  than  he  possesses,  he  is  discontented ; 
if  he  is  discontented,  he  is  unhappy ;  therefore  if  a  man 
is  avaricious,  he  is  unhappy.  This  argument  is  hypo- 
thetical in  form  only,  and  may  be  easily  reduced  to 
categorical  type  as  follow^  •  — 

An  avaricious  man  is  one  who  desires  more  than  he  possesses, 
A  man  who  desires  more  than  he  possesses  is  discontented, 
A  discontented  man  is  unhappy. 

The  efore  -.n  avaricious  man  is  unhappy. 

It  will  be  noticed  that  the  subject  of  the  first  premise 
in  this  form  of  argument  is  taken  as  the  subject  of  the 
conclusion,  and  that  the  predicate  of  the  conclusion  is 
the  predicate  of  the  last  promise.  This  is  usually  called 
the  AristoteHan  sorites.  But  there  is  another  form 
which  unites  in  the  conclusion  the  subject  of  the  last 
premise,  and  the  predicate  of  the  first,  and  which  is 
known  as  the  Goclenian  sorites.^  This  may  be  thus 
represented :  — 


All  A  is  B 

All  C  is  A 

All  D  is  C 

All  E  is  D 

All  E  is  B. 


w  V  V. 


4-U 


Since  B  is  the  predicate  of  the  conclusion,  the  prem- 
ise in  which  it  appears  is  always  to  be  regarded  as  the 
major.     As  a  result  of  this,  it  is  to  be  noticed  that  the 

^  Rudclf  Goclenius  (i  547-1 628),  Professor  at  Marburg,  first  explained 
this  form  in  his  Isagoge  in  Orgamwi  Aristollis,  1 598. 


I! 


\  I 


I':; 


V 


n 


'  1 


BOH 


a 


— •   _«.       ^-Mftz:-, 


^      '       I 


! 


!  I 


.ii: 


132 


FORMS   OF  ARGUMENT 


suppressed  conclusions  in  this  argument  form  the  major 
premise  of  the  following  syllogism,  instead  of  the  minor 
premise  as  in  the  Aristotelian  sorites.  Wc  may,  there- 
fore, expand  the  reasoning  into  the  three  following- 
syllogisms  :  — 


Firs  I'  Syllogism 
All  A  is  B 
All  C  is  A 


Second  Syllogism 
All  C  is  13 
All  D  is  C 


All  C  is  B. 


•.  All  D  is  B. 


Third  Syllogism 
All  D  is  B 
All  E  is  D 

.-.  All  E  is  B. 


A  little  consideration  of  the  form  of  these  syllogisms 
will  lead  the  student  to  se-^^  that  the  rules  given  for  the 
Aristotelian  sorites  must  be  here  reversed.  In  both 
forms  of  the  sorites  there  cannot  be  more  than  one 
negative  premise,  nor  more  than  one  particular  premise. 
In  the  Aristotelian  form,  no  premise  except  the  last  can 
be  negative,  and  no  premise  except  the  first  particular. 
In  the  Goclenian  sorites,  on  the  other  hand,  the  single 
premise  which  can  be  negative  is  the  first,  and  it  is  the 
last  alone  which  may  be  particular. 

§  38.  Irregular  Ar|^uments.  —  There  are  a  large  num- 
ber of  arguments  employed  in  everyday  life  which  are 
valid  and  convincing,  and  yet  which  cannot  be  reduced 
to  the  syllogistic  form.  The  difficulty  with  these  argu- 
ments is  that  they  appear  to  have  four  terms,  at  least  in 
the  form  in  which  they  are  most  naturally  stated.  We 
may  discuss  such  irregular  forms  of  reasoning  under 
two  headings:  (i)  Arguments  which  deal  with  the 
relations  of  things  in  time  and  space,  or  with  theii 
quantitative  determinations;    (2)  arguments  which  are 


M\  E  is  Ji. 


§  38.     IRRECJULAR  ARGUMENTS 


133 


lar^^cly  verbal  in  character,  and  may  be  said  to  depend 
upon  the  principle  of  substitution. 

(i)   As  an  example  of  the  first  class  of  argument  we 
may  take  the  following  :  — 

A  is  greater  than  B, 
B  is  greater  than  C, 


Therefore  A  is  still  greater  than  C. 

It  is  obvious  that,  although  we  have  here  four  terms, 
the  conclusion  is  valid,  and  the  form  of  argument  per- 
fectly convincing.  The  truth  seems  to  be  that  in  rea- 
soning about  quantities  wc  do  not  proceed  upon  the 
syllogistic  principle  of  the  inclusion  and  exclusion  of 
terms.  But  knowing  the  continuous  nature  of  quantity, 
we  take  as  our  principle  that,  '  what  is  greater  than  that 
which  is  greater  than  another  is  a  fortiori  greater  than 
that  other.'  It  would  not,  however,  make  the  matter 
any  clearer  to  write  this  as  our  major  premise,  and 
bring  the  real  argument  under  it  in  this  way  :  — 

What  is  greater  than   that   which    is  greater  than  another  is 
still  greater  than  that  other, 

A  is  that  which  is  greater  than  that  which  is  greater  than  C, 

Therefore  A  is  still  greater  than  C. 

What  we  have  here  given  as  the  major  premise  is 
simply  a  statement  of  the  nature  of  quantity,  not  a 
promis '  from  which  the  conclusion  is  derived.  We  find 
the  same  irregularity  in  arguments  referring  to  the  rela- 
tions of  things  in  space  and  time :  — 

A  is  situated  to  the  east  of  B, 
B  is  situated  to  the  east  of  C, 

Therefore  A  is  to  the  east  of  C. 


t'3 


li 


ti'i:|i|l 


:. '.«! , 

1 

s 

i 

1 

1 

I'-y, 


^1^- 

p 


-3Pi 


r' 


■?H!S" 


■■PI" 


134 


FORMS   OF  ARGUMENT 


lii 


'■(  !i 


f 


iih 


In  spite  of  the  formal  deficiency  of  four  terms  the 
argument  is  valid.  It  will  be  observed,  too,  that  it  is 
in  virtue  of  the  comparison  of  the  position  of  A  and 
of  C  with  that  of  B,  that  these  relative  positions  have 
been  determined.  The  principle  upon  which  we  pro- 
ceed may  be  said  to  be  that,  *  what  is  to  the  east  of  B 
is  to  the  east  of  that  which  B  is  to  the  east  of.'  Or 
perhaps  it  would  be  truer  to  fact  to  say  that  we  proceed 
in  such  cases  upon  what  we  know  regarding  the  nature 
of  space,  and  the  relations  of  objects  in  space. 

(2)  The  second  class  of  irregular  arguments  arc 
largely  verbal  in  character,  and  may  be  dealt  with  very 
briefly.     As  an  example  we  may  consider :  — 

Men  are  willing  to  risk  their  lives  for  gold, 
Gold  cannot  buy  happiness, 

Therefore  men  are  willing  to  risk  their  lives  for  what  cannot  buy 
happiness. 

It  is  doubtful,  I  think,  whether  these  propositions  rep 
resent  any  real  inference.  The  whole  process  may 
be  regarded  as  a  verbal  substitution  in  the  major  prem- 
ise of  'what  cannot  buy  happiness'  for  the  word  'gold.' 
By  a  slight  change  in  the  form  of  the  proposition,  how- 
ever, the  argument  may  be  expressed  as  a  regular 
syllogism  of  the  third  figure :  — 

Gold  is  something  for  which  men  are  willing  to  risk  their  lives. 
Gold  cannot  buy  happiness, 

Therefore  something  which  cannot  buy  happiness  is  somethins^^ 
for  which  men  are  willing  to  risk  their  lives. 

Another  example  which  abso  appears  to  be  irregular 
at  first  sight  is  added  :  — 


^UHij«K<.  I 


M^Ul.'^ 


J  the  nature 
:e. 

fuments   are 
lit  with  very 


liat  cannot  buy 

ositions  rep 
Drocess  may 
major  prem- 
word  *  gold.' 
osition,  how- 
,s  a   regular 


§  38.     IRREGULAR   ARGUMENTS 


135 


The  men  of  the  Middle  Ages  were  ready  to  undertake  any  expe- 
dition where  glory  could  be  won, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

The  crusades,  therefore,  were  readily  undertaken  by  the  men  of 
the  Middle  Ages. 

This  argument  seems  to  be  irregular  in  form  only,  and 
by  a  slight  change  in  form  may  be  expressed  in  the  first 
figure .  — 

All  expeditions  in  which  glory  could  be  won  were  readily  under- 
taken by  the  men  of  the  Middle  Ages, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

Therefore  the  crusades  were  readily  undertaken  by  the  men  of 
the  Middle  Ages. 

References,  especially  for  §  38 

W.  S.  Jevons,  Elcmcnf.a}y  Lessons  in  Logic,  p.  152. 
"    '^        "         'The  Principles  of  Science.  Introduction. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  348-360. 


.»  '■ 


risk  their  lives. 


,s  is  something 


m 


CHAPTER   XI 

HYPOTHETICAL    AND    DISJUNCTIVE    ARGUMENTS 

§  39.  The  Hypothetical  Syllogism.  —  Wc  have  hitherto 
been  dealing  with  syllogisms  composed  entirely  of  cate- 
gorical propositions,  and  have  not  referred  to  the  use 
which  is  made  of  conditional  propositions  in  reasoning. 
A  conditional  proposition  is  sometimes  defined  as  the 
union  of  two  categorical  propositions  by  means  of  a 
conjunction.  It  is  the  expression  of  an  act  of  judg- 
ment which  does  not  directh'  or  unambiguously  assert 
something  of  reality.  We  have  already  pointed  out 
(§  20)  that  there  are  two  classes  of  conditional  propo- 
sitions :  the  JiypotJictical  and  the  disjunctive,  and  corre- 
sponding to  these  we  have  the  hypothetical  and  the 
disjunctive  syllogism.  The  hypothetical  syllogism  has 
a  hypothetical  proposition  as  a  major  premise,  and  a 
categorical  proposition  as  a  minor  premise.  The  dis- 
junctive syllogism  in  the  same  way  is  composed  of  a 
disjunctive  proposition  as  major,  and  a  categorical 
proposition  as  minor,  premise.  In  addition  to  these, 
we  shall  have  to  treat  of  another  form  of  argument 
called  the  'dilemma,'  which  is  made  up  of  hypothetical 
and  disjunctive  propositions. 

A  hypothetical  proposition  asserts  something  not  di- 
rectly, but  subject  to  some  limitation  or  condition.  It 
is   usually   introduced    by   some   word   or   conjunctive 

136 


§39.     ini'   IIYroTIlKTICAL  SVLLnOISM 


137 


phrase,  like  'if,'  'supposin*;,'  or  'granted  that';  as,  ^.,<j\y 
'if  he  were  to  be  trusted,  we  might  give  him  the  mes- 
sage'; 'suppose  that  A  is  B,  then  C  is  D.'  The  part  of 
a  hypothetieal  proposition  which  expresses  the  suppo- 
sition or  condition  is  known  as  the  Antecedent ;  the 
clause  stating  the  result  is  called  the  Consequent.  Thus, 
in  the  proposition,  'he  would  write  if  he  were  well,'  the 
consequent,  *  he  would  write,'  is  stated  first,  and  the 
antecedent,  *  if  he  were  well,'  follows. 

The  hypothetical  syllogism,  as  has  been  already  re- 
marked, has  a  hypothetical  proposition  as  its  major,  and 
a  categorical  proposition  as  its  minor,  premise  :  — 

If  justice  is  to  prevail,  liis  innocence  will  be  proved, 
And  justice  will  prevail, 

Therefore  his  innocence  will  be  proved. 

It  will  be  noticed  that  in  this  argument  the  minor 
})remise  affirms  tJic  antecedent,  and  that,  as  a  residt, 
the  conclusion  affirms  the  consequent.  This  form  is 
known  r.s  the  constnictivc  liypotJictical  syllogism,  or  the 
modus  ponois. 

In  the  following  example  it  will  be  observed  that  the 
consequent  is  denied,  and  the  conclusion  obtained  is 
therefore  negative. 

F he  were  will,  he  would  write, 
He  has  not  written, 


Therefore  he  is  not  well. 


This  is  called  the  destructive  hypotJtetical  syllogism^  or 
modus  tollens. 

The  rule  of  the  hypothetical  syllogism  may  therefore 
be  stated  as  follows  :    EitJier  affirm  the   antecedent  or 


'    X 


1! 


■'  ^  H 


t 


i. 


H 


i^  1 


Hi 


}  ► 


i 


i: 


138     IIYroTllKTICAL   AND    DISJUNCTIVE   ARGUME.JTS 

dc'/iy  iJic  cofiscijficnt.  If  wc  affirm  the  antecedent,  i.e., 
declare  that  the  condition  exists,  the  consequent  neces- 
sarily follows.  And,  on  the  other  hand,  if  the  conse- 
quent is  declared  to  be  non-existent,  we  are  justified 
in  denying  that  the  condition  is  operative. 

The  violation  of  these  rules  gives  rise  to  the  fallacies 
of  denying  tJic  antecedent,  and  of  affirming  the  consequent. 
Thus,  for  example,  we  might  argue  :  — 

If  he  were  well,  he  would  write, 
But  he  is  not  well. 


Tliv.reiore  he  will  not  write. 

'\\Q.rz  the  antecedent  is  denied,  and  the  argument  plainly 
false.  For  we  cannot  infer  that  his  being  well  is  the 
only  condition  under  which  he  would  write.  We  do 
not  know,  in  other  wcrds,  that  the  antecedent  stated 
here  is  the  only,  or  essential  condition  of  the  conse- 
quent. We  know  that  if  there  is  fire,  there  must  be 
heat ;  but  we  cannot  infer  that  there  is  no  heat  when 
no  fire  is  present.  Of  course,  if  we  can  bs  certain 
that  our  antecedent  expresses  the  essential  condition,  or 
real  sine  qua  non  of  the  consequent,  vv^e  can  go  from 
the  denial  of  the  former  to  that  of  the  latter.  For 
example :  — 

If  a  tilangle  is  equilateral,  it  is  also  equiaiigwar,      > 
Th:.r  triangle  is  not  equilateral,  , 

Therefore  it  is  not  equiangular. 

Usually,  however,  when  the  hypothetical  form  of  ex- 
pression is  em.ployed,  we  cannot  be  certain  that  the 
antecedent  expresses  the  sole,  or  essential  condition,  of 
the  consequent.     At  the  ordinary  stages  of  knowledge 


j40.  CATKGORICAL  AND   HYPOTHETICAL  ARGUMP:NTS     I  39 

\vc  have  to  content  ourselves  with  reasoninjj;  from  ante- 
cedent conditions,  without  being  able  to  show  that  no 
other  condition  is  possible. 

To  illustrate  the  fallacy  of  affirming  the  consequent, 
we  may  take  the  following  example  :  — 

If  perfect  justice  prevailed,  the  rich  would  not  be  permitted  to  rob 
the  poor. 

But  the  rich  are  not  permitted  to  rob  the  poor, 


Therefore  perfect  justice  prevails. 

Here  it  will  be  noticed  that  the  consequent  states  only 
our  result  of  the  prevalence  of  *  perfect  justice.'  Be- 
cause the  consequent  is  declared  to  exist,  it  by  no 
means  follows  that  it  exists  as  a  consequence  of  the 
operation  of  this  condition.  It  is  also  worth  noting 
in  this  example  that  the  consequent  of  the  major  prem- 
ise is  negative.  The  minor  premise  which  affirms  the 
consequent  also  takes  a  negative  form.  To  deny  the 
consequent  we  should  have  to  say,  '  the  rich  are 
permitted  to  rob  the  poor.'  Or,  to  put  the  matter  gen- 
erally, it  is  necessary  to  remember  that  the  affirmation 
of  a  negative  proposition  is  expressed  by  a  negative 
proposition,  and  that  the  denial  of  a  negative  —  the 
negation  of  a  negation  —  is,  of  course,  positive  in  form. 


§  40.  ■Relation  of  Categorical  and  Hypothetical  Argu- 
ments. —  It  is  evident  that  the  form  of  the  hypothetical 
syllogism  is  very  different  from  that  of  the  categorical. 
But,  although  this  is  the  case,  it  must  not  be  sup])osed 
that  with  the  former  we  have  passed  to  a  new  and 
wholly    distinct   type    of    reasoning.       In    hypothetical 


-..„  i 


natti 


r  I 


140    iivi'orin:TiCAL  and  DisjUiXcrivi':  AUdUMLOxTS 

reasoning,  ns  in  categorical,  it  is  the  jircscnco  of  a 
universal  [)rinciple  vvhicli  enables  us  to  bring  two  facts 
into  relation  which  formerly  stood  apart.  Indeed,  in 
many  cases,  it  is  a  matter  of  indifference  in  which  form 
the  argument  is  stated.  Thus,  we  may  argue  in  hypo- 
thetical form  :  — 

If  a  man  is  industrious,  he  will  be  successful, 
A  is  an  industrious  man, 

Therefore  A  will  be  successful. 

The  same  argument  may,  however,  be  expressed  equally 
well  in  categorical  form  :  — 

All  industrious  men  will  be  successful. 
A  is  an  industrious  man, 


Therefore  A  will  be  successful. 

It  is  clear  that,  in  spite  of  the  different  forms  in  which 
the  argument  is  exp.cssed,  the  reasoning  is  es.sentially 
the  same  in  both  cases.  The  middle  term,  or  general 
principle  which  makes  it  possible  to  unite  the  subject 
and  predicate  of  the  conclusion,  in  the  hypothetical  as 
well  as  in  the  categorical  syllogism,  is  *  industrious.'  A 
will  be  successful,  we  argue,  because  he  is  industrious, 
and  it  is  a  rule  that  industrious  men  are  successful. 

Moreover,  if  an  argument  is  fallacious  in  one  form,  it 
will  also  be  fallacious  when  expressed  in  the  other. 
The  defects  of  an  argument  cannot  be  cured  simply 
by  a  change  in  its  form.  When  a  hypothetical  argu- 
ment, in  which  the  antecedent  is  denied,  is  expressed 
categorically,  we  have  the  fallacy  of  the  illicit  major 
term.  Thus,  to  state  the  example  of  denying  the  ante- 
cedent given  on  page  138,  we  get:  — 


I 


Mi:xrs 

scncc  of  a 
j^  two  facts 
Indeed,  in 
which  form 
ue  in  hypo- 

cssful, 


;scd  equally 


■ns  in  vvhicli 
essentially 
,  or  general 
the  subject 
othetical  as 
trious.'  A 
industrious, 
:essful. 
one  form,  it 
the  other, 
u'ed  simply 
tical  argju- 
cxpressed 
llicit  major 
ig  the  ante- 


j 


§40.  CATKC.ORICAL  AND   llVroTIIEriCAL   ARGUMENTS     I4I 

Tlie  case  of  his  bein^  well  is  a  case  of  his  uritin;;. 
The  present  is  not  a  case  of  his  bein^  well, 

Therefore  the  present  is  not  a  case  of  his  writing. 

Similarly,  when  an  argument  in  which  the  consequent 
is  affirmed  is  changed  to  the  categorical  form,  the 
di.'fect  in  the  reasoning  appears  as  the  fallacy  of  un- 
distributed middle  :  — 

If  this  tree  were  an  oak,  it  woiiUl  have  roui^h  bark  and  acorns. 
This  tree  has  rough  bark  and  acorns, 

Therefore  it  is  an  oak. 

When  this  argument  is  expressed  in  categorical  form, 
it  is  at  once  clear  that  the  middle  term  is  not  distributed 
in  either  the  major  or  minor  premise :  — 

All  oak  trees  are  trees  having  rough  bark  and  acorns, 
This  tree  is  a  tree  having  rough  bark  and  acorns. 

Therefore  this  tree  is  an  oak. 

The  change  from  the  categorical  to  the  hypothetical 
form  of  argument,  then,  does  not  imjDly  any  essential 
change  in  the  nature  of  the  reasoning  process  itself. 
Nevertheless,  it  is  important  to  note  that  hypothetical 
propositions  and  hypothetical  arguments  emphasize  one 
aspect  of  thinking,  which  is  entirely  neglected  by  the 
theory  of  the  categorical  syllogism.  When  dealing  with 
the  extension  of  terms  (§  16),  we  pointed  out  that  every 
term,  as  actually  used  in  a  proposition,  has  both  an  ex- 
tensive and  an  intensive  function.  That  is,  the  terms  of 
a  proposition  are  employed  both  to  name  certain  objects 
or  groups  of  objects,  and  to  connote  or  imply  certain 
attributes  or  qualities.  In  the  proposition,  'these  arc 
oak  trees,'   the  7/idi/i  purpose   is  to  identify  the  trees 


i  1    #  ! 


l# 


H.I 


''     H 


t 


..i 


142     IIYI'OrilE'nCAL   AND    DISJUNLTIVIC   AKGUMKNTS 


I      i     ! 


given  in  perception  with  the  class  of  oak  trees.  When, 
on  the  other  hand,  we  say,  '  ignorant  people  are  super- 
stitious,' the  proposition  does  not  refer  directly  to  any 
particular  individuals,  but  states  the  necessary  con- 
nection between  ignorance  and  superstition.  Although 
the  existence  of  ignorant  persons  who  are  also  super- 
stitious is  prcsupposcii  in  the  proposition,  its  most 
prominent  function  is  to  assert  a  connection  of  at- 
tributes which  is  wholly  impersonal.  We  may  perhaps 
say  that,  in  spite  of  the  categorical  form,  the  proposition 
is  essentially  hypothetical  in  character.  Its  meaning 
might  very  well  be  expressed  by  the  statement,  'if  a  man 
is  ignorant,  he  is  also  superstitious.'  What  is  here 
emphasized  is  not  the  fact  that  ignorant  persons  exist, 
and  are  included  in  the  class  of  superstitious  persons, 
but  rather  the  general  law  of  the  necessary  connection 
of  ignorance  and  superstition.  The  existence  of  indi- 
viduals to  whom  the  law  applies  is,  of  course,  presup- 
posed by  the  proposition.  It  is  not,  however,  its  main 
purpose  to  directly  affirm  their  existence. 

We  have  reached,  then,  the  following  position : 
Every  judgment  has  two  sides,  or  operates  in  two  ways. 
On  the  one  hand,  it  asserts  the  existence  of  individual 
things,  and  sets  forth  their  qualities  and  relations  to 
other  things.  But,  at  the  same  time,  every  judgment 
seeks  to  go  beyond  the  particular  case,  and  to  read  off  a 
general  law  of  the  connection  of  attributes  or  qualities 
which  shall  be  true  universally.  In  singular  and  par- 
ticular propositions,  the  categorical  element  —  the  direct 
assertion  of  the  existence  of  particular  objects  —  is  most 
prominent,  although  even  here  the  hint  or  suggestion 


§40.  CATEGORICAL  ASM)    HYPOTHETICAL  ARGUMENTS     143 

of  a  <^oncral  hivv  is  not  altogether  absent.  When  we 
reach  the  universal  proposition,  however,  the  reference 
to  real  things  is  much  less  direct,  and  the  meaning 
seems  capable  of  expression  in  hypothetical  form. 

Now  in  the  chapters  on  the  categorical  syllogism 
this  latter  aspect  of  judgments  has  been  left  out  of 
account.  Propositions  were  there  interpreted  as  refer- 
ring directly  to  objects,  or  classes  of  objects  (cf.  §  23). 
The  proposition,  S  is  P,  for  example,  was  taken  to 
affirm  thaf  some  definite  object,  or  class  of  objects, 
S,  falls  within  the  class  P.  And  the  fact  that  it 
is  possible  to  apply  this  theory  shows  that  it  repre- 
sents one  side  of  the  truth.  But  the  student  must 
sometimes  have  felt  that,  in  this  procedure,  the  most 
important  signification  of  the  proposition  is  lost  sight 
of.  It  seems  absurd  to  say,  for  example,  that  in  the 
j)roposition,  '  all  material  bodies  gravitate,'  the  class  of 
'  material  bodies.'  is  included  in  the  wider  class  or 
'things  that  gravitate.'  The  main  purpose  of  the  judg- 
ment is  evidently  to  affirm  the  necessary  connection 
of  the  attributes  of  materiality  and  gravitation.  The 
judgment  does  not  refer  directly  to  things,  or  classes  of 
things  at  all,  but  asserts  without  immediate  reference  to 
any  particular  object,  //material,  then  gravitating.  The 
propositions  of  geometry  are  still  more  obviously  hypo- 
thetical in  character.  '  The  three  angles  of  a  triangle 
are  equal  to  two  right  angles,'  for  example,  cannot, 
without  violence,  be  made  to  mean  that  the  subject  is 
included  in  the  class  of  things  which  are  equal  to  two 
right  angles.  The  main  purpose  of  the  proposition 
is    obviously   to    assert    the    necessary   connection    of 


Nfi' 


y 


\\ 


\ 


« 


V. 


■e 


I 'I 


i    i 


ll 


ll  i 


i 

j 
[ 

■    i 

li 

^                '1 

1  ■          ; 

\  ''■ 

.1 

1            ' 

I  I 

144     IIYrorilKTICAL  AND    DISJUNCTIVE  ARGUMENTS 

the  '  triaiii^ularity '  and  the  equality  of  angles  with 
two  right  angles,  and  not  to  make  any  direet  asser- 
tion regarding  any  actually  existing  object  or  grou}) 
of   objects. 

We  reach,  then,  the  following  conclusion :  Our 
thought  is  at  once  both  categorical  and  hypothetical. 
As  categorical,  it  refers  directly  to  objects  and  their 
relations.  The  terms  of  the  proposition  are  then  taken 
in  extension  to  represent  objects  or  groups  of  objects, 
and  the  copula  to  assert  the  inclusion  of  the  subject  in 
the  predicate,  or,  in  cases  of  negative  propositions,  to 
deny  this  relation.  As  hypothetical,  the  reference  to 
things  is  much  more  indirect.  The  terms  of  the  propo- 
sition are  n  longer  regarded  as  representing  objects  or 
classes,  but  are  interpreted  from  the  point  of  view  of 
intension.  The  judgment  afifirms  or  denies  the  con- 
nection of  the  qualities  or  attributes  connoted  by  the 
terms,  and  not  that  of  the  objects  which  they  denote. 
Sometimes  the  one  aspect  of  thought,  sometimes  the 
other,  is  most  prominent. 

In  sense-perception  and  in  simple  historical  narra- 
tion, assertions  are  made  directly  and  categorically 
regarding  things  and  events  The  main  interest  is  in 
particular  objects,  persons,  or  events,  and  our  judgments 
refer  directly  and  .mambiguously  to  them.  But,  as  \vc 
have  already  seen,  our  thought  from  its  very  beginnini; 
attempts  to  get  beyond  the  existence  of  particular  thin,L,^s 
and  events,  and  to  discover  what  qualities  of  objects  arc 
necessarily  connected.  We  pass  from  perception  and 
observation  to  cxjilanation,  from  the  narration  of  events, 
to  the  discovery  of  the  law  of  their  connection.     And. 


§41-     DISJUNCTIVE   AKGUMEMS 


M5 


as  a  result  of  this  advance,  our  judgments  deal  no  longer 
exclusively  with  particular  objects  and  events,  and  the 
tact  of  their  relation,  but  with  the  general  laws  of  the 
connection  between  attributes  and  c|ualities.  There  is, 
of  course,  no  fixed  point  at  which  we  pass  from  the 
categorical  to  the  hypothetical  aspect  of  thinking.  But, 
in  general,  as  we  pass  from  judgments  of  sense-i:)ercep- 
tion  and  memory,  to  a  statement  of  theories  and  laws, 
the  hypothetical  clement  comes  more  and  more  clearly 
into  the  foreground.  We  have  seen  that  it  is  almost 
impossible  to  interpret  propositions  regarding  geometri- 
cal relations  as  referring  directly  to  classes  of  objects. 
In  the  same  way,  it  is  evident  that  propositions  which 
state  general  laws  are  more  truly  hypothetical  than  cate- 
gorical. When  we  assert  that  '  all  men  are  mortal,'  the 
proposition  does  not  intend  to  state  a  fact  in  regard  to 
each  and  every  man,  or  to  refer  directly  to  individuals 
at  all,  but  to  express  the  essential  and  necessary  relation 
between  humanity  and  mortality.  A  proposition  which 
is  essentially  hypothetical  in  character,  may  then  be 
expressed  in  categorical  form.  It  must  be  remembered 
that  it  is  not  the  form,  but  the  purpose  or  function  of  a 
proposition,  which  determines  its  character.  The  hy- 
j^othetical  form,  however,  does  justice  to  an  aspect  of 
thought  which  is  especially  prominent  in  the  universal 
laws  and  formulas  of  scientific  knowledge,  and  which 
is  ::ot  adequately  represented  by  the  theory  of  subsump- 
tion,  or  the  inclusion  of  the  subject  in  the  predicate. 

§41.   Disjunctive  Arguments.  —  A  disjunctive   propo- 
sition, as  we  have  already  seen,  is  of  the  form,  *A  is 

L 


y 


t    ii 


\l 


?j 


''     N| 


J'  / 


ffiSB 


li 


'     II 


/         i: 


146    liVPO'llIETICAL  AND   DISJUNCTIVE  ARGUMENTS 

either  B,  or  C,  or  D ' ;  or,  \vh;Mi  expressed  negatively, 
*  A  is  neither  B,  nor  C,  nor  1).'  It  is  sometimes  siiid  to 
be  the  union  of  a  caLegorical  and  a  hypothetical  propo- 
sition. On  the  one  hand,  it  asserts  categorically  regard- 
ing A,  and  without  reference  to  any  external  condition. 
But  the  disjunctive  proposition  is  not  simple  like  the 
categorical  proposition  :  it  states  its  results  as  a  series 
of  related  conditions  and  consequences.  If  A  is  not  B, 
it  tells  us,  it  must  be  either  C  or  D ;  and  if  it  is  C,  it 
follows  that  it  cannot  be  B  or  D. 

A  disjunctive  proposition  may  at  first  sight  appear  to 
be  a  mere  statement  of  ignorance,  and,  as  such,  to  be 
less  useful  than  the  simple  categorical  judgment  of  per- 
ception. And  it  is  true  that  the  disjunctive  foim  may 
be  employed  to  express  lack  of  knowledge.  '  I  do  not 
know  whether  this  tree  is  an  oak  or  an  ash ' ;  '  he  will 
come  on  Monday  or  some  other  day.'  A  true  disjunc- 
tive proposition,  however,  is  not  a  mere  statement  of 
ignorance  regarding  the  presence  or  absence  of  sonic 
fact  of  perception.  It  is  an  attempt,  on  the  part  of 
intelligence,  to  determine  the  whole  series  of  circum- 
Stances  or  conditions  within  which  any  fact  of  percep- 
tion may  fall,  and  to  state  the  conditions  in  such  a 
v^ay  that  their  relations  are  at  once  evident.  And  to 
do  this  implies  positive  knowledge.  In  the  first  place, 
the  enumeration  of  possibilities  must  be  exhaustive, 
no  cases  must  be  overlooked,  and  no  circumstances 
left  out  of  account.  Secondly,  the  members  of  the 
proposition  must  be  taken  so  as  to  be  really  disjunc- 
tive. That  is,  they  must  be  exclusive  of  one  another. 
We  cannot  combine  disjunctively  any  te»"ms  we  please 


ENTS 

legatively, 
les  said  to 
cal  propo- 
Uy  regard- 
condition, 
e  like  the 
as  a  series 
\  is  not  B, 
it  is  C,  it 

t  appear  to 
such,  to  be 
iient  of  per- 
j  foun  may 
*  I  do  not 
1 ' ;  'he  will 
rue  disjunc- 
atement  of 
ice  of  sonic 
the  part  ot 
of  circum- 
of  percep- 
in   such  a 
nt.     And  to 
first  place, 
exhaustive, 
rcumstanccs 
ibers  of   the 
ally  disjunc- 
ne  another, 
is  we  please 


§  41.     DISJUNCTIVE   ARGUMENTS 


147 


with  each  other.  But  it  is  only  when  we  understand 
the  systematic  connections  of  things  in  the  field  in  ques- 
tion, that  we  are  able  to  express  them  in  the  form  cither 
B  or  C,  and  thus  assert  that  the  presence  of  one  ex- 
cludes the  other. 

A  disjunctive  proposition,  then,  presupposes  syste- 
matic knowledge,  and  is  consequently  the  expression  of 
a  comparatively  late  stage  in  the  evolution  of  thought. 
It  is  true  that  disjunction  may  involve  doubt  or  igno- 
rance regarding  any  particular  individual.  We  may 
not  be  able  to  say  whether  A  is  B  or  C  or  D.  I^ut, 
before  we  can  formulate  the  disjunctive  proposition, 
we  must  be  already  acquainted  with  the  whole  set  of 
possible  conditions,  and  also  with  the  relation  in  which 
those  conditions  stand  to  each  other.  Our  knowledge, 
when  formulated  in  the  disjunctive  major  premise  of 
an  argument,  is  so  exhaustive  and  systematic,  that 
the  application  to  a  particular  case  effected  by  the 
minor  premise  appears  almost  as  a  tautology.  This 
will  be  evident  in  the  disjunctive  arguments  given 
below. 

There  are  two  forms  of  the  disjunctive  syllogism. 
The  first  is  sometimes  called  the  tnodus  tollcndo  poticns, 
or  the  mood  which  affirms  by  denying.  The  minor 
premise,  that  is,  is  negative,  and  the  conclusion  affirma- 
tive.    The  form  is,  — 

A  is  either  B  or  C, 
A  is  not  C, 

Therefore  A  is  B. 

The  negative  disjunctive  argument  has  an  aflfirmative 
minor   premise.     It   is    known   as   the    uiodus  poncndo 


(,11  1 


-a 


!Ril 


n 


i  l' 


mi 


148     HVPOrilETICAL   AND    DISJUNCTIVE   AKCJUMKNTS 

toUcnSy  or  the  form  which,  Ijy  affirmin<^  one  member  of 
the  disjunctive  series,  denies  the  others,  — 

A  is  H  or  C  or  U, 

But  A  is  I}, 

Therefore  A  is  neither  C  nor  D. 
It  is,  of  course,  a  very  simple  matter  to  draw  the  con- 
clusion from  the  premises  in  these  cases.  As  we  have 
already  indicated,  the  real  intellectual  work  consists  in 
obtaining  the  premises,  especially  in  discovering  the 
relations  enumerated  in  the  major  premise.  It  is  in 
formulating  the  major  premise,  too,  that  errors  are  most 
likely  to  arise.  As  already  pointed  out,  it  is  essential 
that  the  disjunctive  members  shall  be  exhaustively 
enumerated,  and  also  that  they  shall  exclude  each  other. 
ViWt  it  is  not  always  easy  to  discover  all  the  possibilities 
of  a  case,  or  to  formulate  them  in  such  a  way  that  they 
are  really  exclusive.  If  we  say,  *he  is  either  a  knave 
or  a  fool,'  we  omit  the  possibility  of  his  being  both  the 
one  and  the  other  to  some  extent.  A  great  many  state- 
ments which  are  expressed  in  the  form  of  disjunctive 
propositions  are  not  true  logical  disjunctives.  Thus  we 
might  say,  'every  student  works  either  from  love  of 
learning,  or  from  love  of  praise,  or  for  the  sake  of  some 
material  reward.'  But  the  disjunction  does  not  answer 
the  logical  requirements,  for  it  is  possible  that  two  or 
more  of  these  motives  may  influence  his  conduct  at 
the  same  time.  The  disjunctive  members  are  neither 
e.xclusive  nor  completely  enumerated. 

§  42.    The   Dilemma.  —  A  dilemma  is   an    argument 
composed  of  hypothetical  and  disjunctive  propositions. 


■^ 


■•m 


1  I 


§42.     TIIK    1)11. KM  MA 


149 


As  the  word  is  used  in  ordinary  life,  \vc  arc  said  to  be  in 
a  dilemma  whenever  there  arc  but  two  courses  of  action 
open  to  us,  and  when  both  of  these  have  unpleasant 
consequences.  In  the  same  way,  the  logical  dilemma 
shuts  us  in  to  a  choice  between  alternatives,  either  of 
which  leads  to  a  conclusion  we  would  gladly  avoid. 

The  first  form,  which  is  sometimes  called  the  Simple 
Constructive  Dilemma,  yields  a  simple  or  categorical  con- 
clusion, — 

If  A  is  R.  C  is  D  ;  and  if  E  is  F,  C  is  D, 
But  either  A  is  B,  or  E  is  F, 


lil 


Therefore  C  is  D. 


lY  a  Knave 


It  will  be  noticed  that  the  minor  premise  affirms  dis- 
junctively the  antecedents  of  the  two  hypothetical  prop- 
ositions which  form  the  major  premise,  and  that  the 
conclusion  follows  whichever  alternative  holds.  We 
may  take  as  a  concrete  example  of  this  type  of  argu- 
ment :  — 

If  a  man  acts  in  accordance  with  his  own  judf];ment.  he  will  he 
criticised;  and  if  he  is  guided  by  the  opinions  and  rules  of  others, 
he  will  be  criticised. 

But  he  must  either  act  in  accordance  with  his  own  judgment,  or 
he  guided  by  the  opinions  of  others. 

Therefore,  in  any  case,  he  will  be  criticised. 

The  hypothetical  propositions  which  make  up  the 
major  premise  of  a  dilemma  do  not  usually  have  the 
same  consequent,  as  is  the  case  in  the  examples  just 
^Mven.  When  the  consequents  involved  are  different, 
the  dilemma  is  said  to  be  complex,  and  the  conclusion 
has  the  form  of  a  disjunctive  proposition.     In  the  Complex 


'.?:'/ 


^ 


-■autt.-  .na. 


! 


t  i 


150     lIYrurilETICAL  AND   DISJUNCTIVE  AKGUMEMS 

Constructive  Dilemma,  the  minor  premise  affirms  disjunc- 
tively the  antecedents  of  the  major,  and  the  conclusion 
is  consequently  affirmative.  We  may  take,  as  an  ex- 
ample, the  argument  by  which  the  Caliph  Omar  is 
said  to  have  justified  the  burning  of  the  Alexandrian 
library :  — 

If  these  books  contain  the  same  doctrines  as  the  Koran,  they  arc 
unnecessary ;  and  if  they  are  at  variance  with  the  Koran,  they  are 
wicked  and  pernicious. 

But  they  must  either  contain  the  same  doctrines  as  the  Koran  or 
be  at  variance  with  it. 


Therefore  these  books  are  eitlier  unnecessary  or  wicked  and  per- 
nicious. 

A  third  form,  the  Complex  Destructive  Dilemma,  obtains 
a  negative  disjunctive  proposition  as  a  conclusion,  by 
denying  the  consequents  of  the  hy})othetical  proposi- 
tions which  form  the  major  premise  of  the  argument. 
We  may  take  the  following  example :  — 

If  a  man  is  prudent,  he  will  avoid  needless  dangers ;  if  he  is  bold 
and  courageous,  he  will  face  dangers  bravely.  ' 

But  this  man  neither  avoids  needless  dangers  nor  does  he  face 
dangers  bravely. 

Therefore  he  is  neither  prudent  nor  bold  and  courageous. 

By  taking  more  than  two  hypothetical  propositions 
as  major  premise,  we  may  obtain  a  Trilemma,  a  Tetra- 
lemma,  or  a  Polylemma.  These  forms,  however,  are 
used  much  less  frequently  than  the  Dilemma. 

The  dilemma  is  essentially  a  polemical  or  contro- 
versial form  of  argument.  Its  object,  as  we  have  seen, 
is  to  force  an  unwelcome  conclusion  upon  an  adversary, 
by  showing  that  his  argument,  or  his  conduct,  admits  of 


H. 


§  42.     THE   DILEMMA 


151 


one  or  other  of  two  unpleasant  interpretations.  W'c 
sometime.s  speak  of  the  horns  of  the  dilemma,  and  of 
our  adversary  as  'gored,'  whichever  horn  he  may  choose. 
Dilemmas,  however,  like  all  controversial  arguments, 
are  more  often  fallacious  than  valid.  The  minor  pre- 
mise of  a  dilemmatic  argument,  as  we  have  already 
seen,  is  a  disjunctive  proposition  with  two  memhers. 
But  it  is  very  rarely  that  two  alternatives  exhaust  all 
the  possible  cases.  The  cases  enumerated,  too,  may 
not  exclude  each  other,  or  be  real  alternatives  at  all. 
The  dilemma  is  thus  sul)ject  to  all  the  dangers  which 
we  have  already  noticed  in  the  case  of  the  disjunctive 
argument.  In  addition,  it  is  necessary  to  see  that  the 
canon  of  the  hypothetical  syllogism,  'affirm  the  ante- 
cedent or  deny  the  consequent,'  is  observed.  If  this 
rule  is  not  observed,  the  logical  form  of  the  argument 
will  not  be  correct. 

References,  especially  for  §  40 

J.  S.  Mill,  Logic,  Uk.  1.  Ch.  V. 
C.  Sigwart,  Loi^u\  I't.  I.  Ch.  \'II. 

VV.    Miiito,    Logic   liuiitciivc  and  Deductive.,  pp.    129-138.  and 
pp.  214-225. 

F.  H.  Bradley,  The  Principles  of  Logic,  Bk.  I.  Ch.  2. 
B.  Bosanquet.  T/ie  Essentials  of  Logic,  Lecture  VL 


il 


\t 


'     N( 


'{      W-      : 

i  1    '^ 

'         1'                ' 

I       1         1       > 

N, 


^1 
'I' 


i   >. 


!-iw— ana 


( 


i; 

t 

i 

it 

i 

^' 


V 


1 

\                         1 

id 

'        ( 

^ 

1 

■ 

1        J 

% 

1' 

1 

\ 

\\ 

1 

ti 

CHAITKR    XII 

FALLACIES  OK  DEDUCTIVE  REASONING 

§  43.  Classification  of  Fallacies.  —  We  shall  hccaiter 
trt'at  of  '  -'  L;  'ajie  .  or  errors  to  :vhich  inductive  reason- 
ing is  riv  ;t  w^nect  (Ch.  xix.).  At  present,  however, 
it  is  necessaiy  to  "^sider  the  fallacies  which  are  likely 
to  attend  the  employment  of  the  syllogistic  form  of 
reasoning.  In  considering  the  subject,  we  shall  find 
that  many  fallacies  belong  equally  to  both  kinds  of 
reasoning.  This  is  especially  true  of  errors  which  arise 
from  the  careless  use  of  words. 

The  first  systematic  account  of  fallacies  is  given  in 
Aristotle's  treatise,  On  Sophistical  Difficulties  {Trepl  aofbia- 
TiKcdv  iX€y)(^ci)v).  In  this  work,  Aristotle  divides  falla- 
cies into  two  classes :  those  which  are  due  to  language 
{Trapa  tt)v  Xc^lv,  or,  as  thoy  are  usually  called,  fallacies 
///  dictionc),  and  those  which  are  not  connected  with  lan- 
guage (e|a)  T?)'^  Xefeo)?,  extra  dictioncni).  Under  the  first 
head,  he  enumerates  six  kinds  of  fallacies,  and  under 
the  second,  seven.  Aristotle's  principle  of  classification 
is,  however,  not  entirely  satisfactory.  We  must  try  to 
find  some  positive  principle  or  principles  of  classification 
which  will  render  us  more  assistance  in  understanding 
the  relations  between  the  various  fallacies  than  is 
afforded  by  Aristotle's  division  into  those  which  belong 
to  language,  and  those  which  do  not. 


I 


c  rcason- 
howcvcr, 
irc  likely 
form  of 
chilli  find 
kinds  of 
lich  arise 

given  in 
epl  ao(hi(T- 
dcs  falh- 
language 

fallacies 
with  lan- 
r  the  first 
nd  under 
ssification 
list  try  to 
ssification 
rstanding 

than    is 
:h  belong 


I 


§43.     Cf.ASSIlIC.vrioN   OF    K.\l-L\(Ii:s 


153 


In  the  strict  sense  ol  the  word,  a  lallacy  is  to  be 
defined  as  an  erroi  in  reasoning.  In  the  syllogism, 
however,  propositions  or  premises  form  the  data  or 
starting-point.  U,  now,  these  j^ropositions  are  not 
properly  rnderstood,  the  conclusions  to  which  they 
lead  a.e  likely  to  be  fal'  v..  We  may  then  first  divide 
fallacies  into  Errorr  of  Interpretation,  and  Fallacies  in 
Reasoning  Errors  in  interpreting  i)ropositions  might, 
perhaps,  be  more  properly  treated  in  a  work  on  rhetoric 
thai,  in  a  chapter  on  logical  fallacies.  But  it  has  been 
the  custom  ever  since  the  time  of  Aristotle  to  include 
in  tlie  enumeration  of  logical  fallacies  a  ni  u/  of 
ernrs  which  are  likely  to  arise  in  interj^reti  "g  \  po- 
sitions. Moreover,  as  we  saw  in  Chapter  '  li  there 
are  certain  ]irocesses  of  interpretation,  like  (;  .version 
and  Conversion,  which  are  sometimes  call  in  ;iicdiatc 
inference,  and  which  recjuire  a  knowledge  ot  the  logical 
structure  of   jiropositions. 

The  Fallacies  which  arise  in  the  process  of  reasoning, 
we  may  again  divide  into  Formal  Fallacies,  or  violations 
of  the  syllogistic  rules,  and  Material  Fallacies.  The 
latter  class  may  be  further  divided  into  Fallacies  of 
Equivocation  (including  Ambiguous  Middle,  Composi- 
tion, Division,  and  Accident)  and  Fallacies  of  Presump- 
tion (including  Pelitio  Principii,  Irrelevant  Conclusion, 
Non  Secpiitur,  and  Complex  Questions).  The  following 
table  will  summarize  this  classification  :  — 


'    f 


« 

V 

1 

■M 

i 

!■  A I -LAC  IKS   OK    I)KI)l'(  nVK    K1-AS(JMNG 


Kam.aciks 


Errors  in  Inttrpfctalion 

(1)  Illogical  Obvcrsion  or 
Conversion 

(2)  Amphiholy 

(3)  Accent 


Misliikes  in  Reasoning 


Material 


In  Categorical 
Arguments 


Formal 

'(l)   Four  Terms 

(2)  Undistriliuted 

Middle 

(3)  Illicit  Major 

(4)  Illicit  Minor 


Equivocation  Presumption 

(1)  Anibif^uous  (l)  Pctitio  Prin- 

Middle  cipii 

(2)  Composition  (2)  Complex 


(3)  Division 

(4)  Accident 


^(5)  Negative  Premises 

(6)   Denying  the  Antecedent 

"'  I  (7)   Aftirining  the  Conseciuent 
Arguments    y"  ^  ' 

In  Disjunctive  j  ^^^   i„,p,rf,ct  Disjunction 
Arguments     ( 


In 

Hypothetical 


(Question 

(3)  Irrelevant 

("onclusion 

(4)  Non  Seciuitur 


§  44.  Errors  in  Interpretation.  —  This  class  of  fallacies 
results  from  imperfect  understanding  of  the  meaning 
of  propositions.  They  are  not,  then,  strictly  speaking, 
errors  of  reasoning  at  all.  If,  however,  the  propositions 
employed  as  premises  in  an  argimient  are  not  correctly 
understood,  the  conclusions  founded  upon  them  are 
likely  to  be  erroneous.  And  even  if  the  proposition, 
which  is  wrongly  interpreted,  is  not  made  the  basis  of 
further  reasoning,  it  is  in  itself  the  result  of  an  intel- 
lectual error  against  which  it  is  possible  to  guard.  We 
do  not,  of  course,  profess  to  point  out  all  the  possible 
sources  of  error  in  interpreting  propositions.     The  only 


§44      KKKOKS   IN    IN  IKKPRKTATIDN 


155 


rule  applicable  to  all  cases  which  can  be  L;iven  is  this  : 
Accept  no  projiositioii  until  you  understand  its  exact 
meaning;,  and  know  precisely  what  it  inii)lies.  Delib- 
eration and  attention,  both  with  re;;ard  to  our  own 
statements  and  those  of  others,  are  the  only  means 
of  escaping  errors  of  this  kind. 

( I )  Il/oqical  Obi'crsion  or  Conversion.  —  In  a  previous 
chapter  (Ch.  vii.),  we  have  treated  of  Obversion  and 
Conversion,  and  shown  the  rules  to  be  followed  in  statin^t; 
the  obverse  or  the  converse  of  a  proposition.  Tn  (Obver- 
sion, we  interpret  or  show  what  is  involved  in  a  proj)osi- 
tion,  by  statinjj;  its  implications  in  a  j)roposition  of  the 
opposite  quality.  And  unless  we  have  clearly  <^rasped 
the  meanin*;  of  the  original  jiroposition,  mistakes  arc 
likely  to  arise  in  changing;  from  the  affirmative  to  the 
ne<;"ative  form  of  statement,  or  from  the  neijative  to  the 
affirmative.  Thus,  we  should  fall  into  an  error  of  this 
kind  if  we  should  take  the  proposition,  '  honesty  is 
always  good  policy,'  to  be  the  cc|uivalcnt  of,  or  to  imply, 
the  statement,  'dishonesty  is  always  bad  policy.'  Nor 
can  we  obtain  by  obversion  the  i)roposition,  '  all  citizens 
are  allowed  to  vote,'  from,  '  no  aliens  are  allowed  to 
vote.' 

In  Conversion,  we  take  some  proposition,  A  is  B,  and 
ask  what  assertion  it  implies  regarding  the  predicate. 
Docs  '  all  brave  men  are  generous '  imj^ly  also  that  '  all 
generous  men  are  brav^e  ' .''  This  is,  perhaps,  the  most 
frequent  source  of  error  in  the  conversion  of  proposi- 
tions. I  do  not  mean  that  in  working  logical  examples 
we  are  likely  to  convert  proposition  \  simply,  instead  of 
by  limitation.     But  in  the  heat  of  debate,  or  when  using 


,1 


.i:(, 


156 


IAI.LA(  IKS   Ol-    DKhlKTIVK    KI:AS(  )NIN(; 


propositions  without  jiropcr  attention,  there  is  a  natural 
tendency  to  assume  that  a  proposition  which  makes  a 
universal  statement  rei^ardinj^  the  subject,  does  the  same 
with  regard  to  the  predicate.  And,  although  such  errors 
are  very  obvious  when  pointed  out,  —  as,  indeed,  is  the 
case  with  nearly  all  logical  fallacies,  —  they  may  very 
easily  impose  ui)on  us  when  our  minds  are  not  fully 
awake,  that  is,  wiien  attention  is  not  active  and  con- 
sciously on  guard.  Of  the  other  methods  of  conversion 
perhaps  contraposition  is  most  likely  to  be  a  source  of 
error.  We  have  already  (§  27)  given  the  rules  for  ob- 
taining the  contrapositive  of  any  proj)osition.  Some 
practice  in  working  examples  will  assist  students  in 
perceiving  what  is  the  logical  contrapositive  to  any 
proposition,  and  in  detecting  fallacies. 

(2)  AuipJiiboIy,  or  amphibology  (afKpi/SoXia),  consists 
in  misconception  arising  from  the  ambiguous  gram- 
matical construction  of  a  i)roposition.  A  sentence  may 
have  two  ojijiosite  meanings,  but  one  may  be  more 
natural  and  prominent  than  the  other.  A  deception 
may  be  i)ractised  by  leading  a  person  to  accept  the 
meaning  more  strongly  suggested,  while  the  significance 
intended  is  the  very  opposite,  as,  r.jr.,  '  I  hoj)e  that  you 
the  enemy  will  slay.'  In  Shakespeare's  Ilony  VI.,  we 
have  an  instance  of  amphiboly  in  the  prophecy  of  the 
spirit,  that  "the  Duke  yet  lives  that  Henry  shall 
depose." 

(3)  The  Fallacy  of  Accent  is  a  misconception  due  to 
the  accent  or  emphasis  being  placed  upon  the  wrong 
words  in  a  sentence.  It  may,  therefore,  be  regarded 
as  a  rhetorical,  rather  than  as  a  logical  fallacy.    Jevons's 


M  : 


§45.     roRMAI,    rAI.I.ACIKS 


•57 


}      It 


aturM 


ukc's  a 
c  same 
1  errors 
,  is  the 
ly  very 
It  fully 
lid  con- 
iversion 
uree  of 

for  ob- 

Somc 

ients   in 

to   any 

consists 
s  gram- 
nce  may 
oe  more 
eception 
cpt  the 
lificance 
that  you 
K/.,  we 
of  the 
ry    shall 

In  due  to 
ie  wroni!; 
'etcarded 
Jevons's 


11 


examples  of  this  fallacy  may  be  (pioted  in  part.  "  A 
ludicrous  instance  is  liable  to  occur  in  reading*  Chapter 
XIII.  of  the  First  Hook  of  Kin^^s,  verse  27,  wher  •  it  is 
said  of  the  prophet,  'And  he  spake  to  his  sons,  sayin<;. 
Saddle  me  the  ass.  And  they  sadilled  //////.'  The  italics 
indicate  that  the  word  ///;//  was  supplied  by  the  trans- 
lators of  the  authorized  version,  but  it  may  su<;j;est  a 
very  different  meaninj^.  The  commandment,  'Thou 
shalt  not  bear  false  witness  aj;ainst  thy  neighbour,'  may 
be  made  by  a  slij^ht  emphasis  of  the  voice  on  the  last 
word  to  imply  that  we  are  at  liberty  to  bear  false 
witness  aj^ainst  other  persons.  Mr.  l)e  Morgan  who 
remarks  this  also  points  out  that  the  erroneous  cpioting 
of  an  author,  by  unfairly  sei)aratin<;  a  word  from  its 
context,  or  italici^dng  words  which  were  not  intended  to 
be  italicized,  gives  rise  to  cases  of  this  fallacy."  ^  Jevons 
is  also  authority  for  the  statement  that  Jeremy  l^entham 
was  so  much  afraid  of  being  led  astray  by  this  fallacy 
that  he  employed  a  person  to  read  to  him  whose  voice 
and  manner  of  reading  were  particularly  monotonous. 

§  45.  Formal  Fallacies.  — We  shall  follow  our  table, 
and  deal  with  mistakes  of  Reasoning  under  the  two 
headings  of  Formal  Fallacies,  and  Material  Fallacies. 
Formal  fallacies  arise  from  violations  of  the  rules  of  the 
syllogism.  The  breaches  of  these  rules  have  been 
already  p-  uted  out,  and  illustrated  in  our  discussion  of 
the  various  iorms  of  syllogistic  argument.  The  analysis 
of  arguments,  with  a  view  to  the  detection  of  such 
fallacies,  where  any  exist,  is  a  very  important  exercise, 

*  Jevons,  Lessons  in  Lo^ic,  p.  1 74. 


i 


ft 

.  1 

i 

jBBlli! 

j; 

1 

1       • 

t 

'•     I 


N  # 


'/' 


158 


I'ALLACIKS   OF   DLDUdlVL    REASONING 


)'*■ 


.11 


and  affords  valuable  mental  discipline.  It  seems  only 
necessary  here  to  add  a  remark  rej^arding  the  first 
fallacy  on  our  list,  that  of  Four  Terms,  or  Qnatcrnio 
'J\'nninonnn,  as  it  is  usuall)'  called  by  logicians. 

The  first  canon  of  the  categorical  syllogism  states 
that  'a  syllogism  must  contain  three  and  only  three 
terms.'  This  rule  would  of  course  be  violated  by  such 
an  argument  as,  — 

Frcnciimen  are  luiropcans, 
I'Lii^lishnnjn  arc  AiiLjIo-Saxons. 


ThcrefDrc  Enj^Hshniun  are  luirtjpeans. 

It  is  so  obvious  that  this  cxami)le  does  not  contain 
a  real  inference  that  no  one  would  l)e  likely  to  be  mi.s- 
led  by  the  pretence  of  argument  which  it  contains.  In 
some  cases,  however,  a  term  may  be  used  in  two  senses, 
although  tlie  words  by  which  it  is  expressed  are  the 
same.     The  following  exami)le  may  be  given  :  — 

Every  good  law  should  he  obeyed, 
The  law  of  j;ravitation  is  a  good  law. 

Therefore  the  law  of  gravitation  should  he  obeyed. 

Here  we  have  really  four  terms.  The  word  'law,'  in 
the  first  proposition,  means  a  command  given  or  enact- 
ment made  by  some  persons  in  authority.  A  '  good 
law'  in  this  sense  then  means  a  just  law,  or  one  which 
has  benehciLil  results.  lUit  in  the  second  proposition 
it  signifies  a  statement  of  the  uniform  way  in  which 
phenomena  behave  under  certain  conditions.  A  'good 
law '  from  this  point  of  view  would  imply  a  correct 
statement  of  these  uniformities.  It  is  interesting  to 
note  that    this  example   may   also  be   regarded  as   an 


is  only 
c  first 
atcniio 

I  states 
^  three 
3y  such 


§  46.     MATKRIAL    FALLACIKS 


159 


instiince  of  lujuivoeation,  and  classified  as  a  case  of  an 
ambiguous  middle  term.  1 1  is  often  possible  to  classify 
a  i'allacy  under  more  than  a  single  head. 

There  are,  however,  cases  where  an  arLjument  may 
seem  at  first  slight  to  have  four  terms,  but  where  the 
defect  is  only  verbal.  The  matter  must,  of  course,  be 
determined  by  reference  to  the  meanin<;  of  terms  and 
not  merely  to  the  verbal  form  of  expression.  It  is  ideas 
or  concepts,  and  not  a  form  of  words,  which  are  really 
operative  in  reasoning. 


contam 
be  mis- 
ins.  In 
)  senses, 

are  the 


1(1. 

law,'  in 
)r  enact- 
A.  '  good 
le  which 
)position 
n  which 
A  ' good 
I  correct 
:sting  to 
d  as   an 


§  46.  Material  Fallacies.  — What  arc  called  material 
fallacies  do  not  result  from  the  violation  of  any  specific 
logical  rules.  They  are  usually  said  to  exist,  iK^t  in  the 
form,  but  in  the  matter  (^{  the  argument.  Consequently, 
it  is  sometimes  argued,  the  detection  and  description  of 
them  do  not  properly  belong  to  logic  at  all.  We  have 
found,  however,  that  all  these  fallacies  have  their 
source  in  ICcpuvocation  and  Presumption.  They  thus 
violate  two  of  the  fundamental  principles  of  logical 
argument.  For  all  logical  reasoning  presupposes  that 
the  terms  employed  shall  be  clearly  defined,  and  used 
throughout  the  argument  with  a  fixed  and  definite 
signification.  And,  .secondly,  logic  rei|iiires  that  the 
conclusion  shall  not  be  a;;sumed,  but  derived  strictly 
from  the  premises.  The  violation  of  these  principles 
is,  therefore,  a  proper  matter  of  concern  to  the  logieian. 
We  shall  treat  first  of  the  fallacies  of  ICquivocation. 

{A)  The  fallacies  of  lC(|uivocation  have  been  enumer- 
ated as  Ambiguous  Middle  Term,  Composition,  Division, 
and  Accident.     These  all  result  from  a  lack  of  clearness 


|i 


P 


i 


■  ( 


n 


'    'r 


(.  I 


^i\ 


ii 


i 


t6o 


FALLACIES  OF   DEDUCTIVE   REASONIXCJ 


and  dcfinitcncss  in  the  terms  employed.     We  shall  deal 
with  them  briefly  in  order. 

(i)  T^e  phrase,  Ambiguous  Middle  Term,  describes 
the  first  uillacy  of  this  group.  It  is  obvious  that  the 
middle  term  cannot  form  a  proper  standard  of  com- 
parison if  its  meaning  is  uncertain  or  shifting.  A 
standard  of  measure  must  be  fixed  and  definite.  One 
illustration  of  this  fallacy  will  be  sufficient :  — 

Partisans  are  not  to  be  trusted, 

Democrats  are  partisans, 

Therefore  Democrats  are  not  to  be  trusted. 
The  middle  term,  '  partisan,'  is  evidently  ured  in  two 
senses  in  this  argument.  In  the  first  premise  it  signifies 
persons  who  are  deeply  or  personally  interested  in  some 
measure;  and  in  the  latter  it  simply  denotes  the 
members  of  a  i)olitical  party.  When  an  argument  is 
long,  and  is  not  arranged  in  syllogistic  form,  this  fallacy 
is  much  more  difficult  of  detection  than  in  the  simule 
example  which  has  been  given.  It  is  of  the  utmost 
importance,  then,  to  insist  on  realizing  clearly  in  con- 
sciousness the  ideas  for  which  each  term  stands,  and  not 
to  content  ourselves  with  following  the  words. 

(2)  The  fallacy  of  Composition  arises  when  we  affirm 
something  to  be  true  of  a  whole,  which  holds  true  only 
of  one  or  more  of  its  parts  when  taken  separately  or 
distributivcly.  Sometimes  the  error  is  due  to  confusion 
between  the  distributive  and  collective  signification  of 
'  all,'  as  in  the  following  example  :  — ■ 

All  the  an<i;les  of  a  triangle  are  less  lh;ui  two  riiijht  an<i[les, 
A,  B,  and  C  are  all  the  angles  t)f  this  triangle. 

Therefore  A,  B,  and  C  are  less  than  two  right  angles. 


tax 

f()]l( 

if  a] 

adva 

than 

they 

be  m 

iiicrc 

i)r()fi( 


:ill  deal 

ascribes 
hat  the 
)f  com- 
•ng.  A 
I.     One 


1  in  two 
signifies 
I  in  some 
otcs    the 
umcnt  is 
is  fallacy 
le  simple 
i   utmost 
in  con- 
and  not 

:e  affirm 
rue  only 

irately  or 
onfusion 

ication  of 

an<;les, 
lies. 


§46.     MATKKIAI.    lAI.LACIES 


ID  I 


It  is,  of  course,  obvious  that  '  all  the  angles  of  a 
triangle '  in  the  major  i)remise  signifies  each  and  every 
angle  when  taken  by  itself,  and  that  the  same  words  in 
the  minor  premise  signify  all  the  angles  collectively. 
What  is  true  of  all  the  jDarts  taken  separately,  is  not 
necessarily  true  of  the  whole.  We  cannot  say  that 
because  no  one  member  of  a  jury  is  very  wise  or  very 
fair-minded,  that  the  jury  as  a  whole  are  not  likely  to 
bring  in  a  just  verdict.  The  members  may  mutually 
correct  and  supplement  each  other,  so  that  the  finding 
of  the  jury  as  a  whole  will  be  much  fairer  and  wiser 
than  the  judgment  of  any  single  individual  composing 
it.  Another  instance  of  this  fallacy  which  is  often 
(|iioted  is  that  by  which  protective  duties  are  sometimes 
supported :  — 

The  manufacturers  of  woollens  are  benefited  by  the  duty  on 
woollen  goods  ;  the  manufacturers  of  ojtton  by  the  duty  on  cotton  ; 
the  farmer  by  the  duties  on  wool  and  grain  ;  and  so  on  for  all  the 
other  producing  classes;  therefore,  if  all  the  products  of  the  country 
were  protected  by  an  import  duty,  all  the  pi  (educing  classes  would 
be  benefited  thereby. 

lUit,  because  each  class  would  be  benefited  by  an  import 
ta.\  ui)on  some  j)articular  product,  it  does  not  necessarily 
follow  that  the  community  as  a  whole  would  be  benefited 
if  all  products  were  thus  protected.  For,  obviously,  the 
advantages  which  any  class  would  obtain  might  be  more 
than  offset  by  the  increased  jjrice  of  the  things  which 
they  would  have  to  buy.  On  the  other  hand,  it  would 
be  necessary  to  take  into  consideration  the  fact  that  an 
increase  in  the  prosperity  of  one  class  indirectly  brings 
profit  to  all  the  other  members  of  the  same  society. 

M 


i 
I' 


.  ih 


''   «« 


.'    I 


u 


t--JUWIIIUIW 


163 


I'ALLACIIOS  OF   I)1:1jL'CHVE  klasoning 


Wo  cannot  rc.i^anl  a  whole  as  sini))ly  a  sum  of  parts, 
l)ut  must  consider  also  tlic  way  in  which  the  parts  act 
and  react  upon  eacli  other. 

(3)  Tile  fallacy  of  Division  is  the  converse  of  Com- 
])osition.  It  consists  in  assuming;  that  what  is  true  of 
the  whole  is  also  true  of  the  jKirts  taken  separately. 
Some  term,  which  is  used  in  the  major  i)remise  collec- 
tively, is  employed  in  a  distributive  sense  in  the  minor 
premise  and  conclusion.  The  following  example  will 
illustrate  this :  — 

All  the  arii^lc's  of  a  triangle  are  ecjual  to  two  right  angles, 
A  is  an  angle  of  a  triangle, 


Therefore  A  is  e([ual  'o  two  right  angles. 

To  ar[;ue  that,  because  some  measure  benefits  the 
country  as  a  whole,  it  must  therefore  benefit  every 
section  of  the  country,  would  be  another  instance  of 
this  fallacy.  Ap^ain,  we  may  often  find  examples  of 
both  Division  and  C(M1i position  in  the  practice  so  com- 
mon in  debate  of  'taking  to  pieces'  the  arguments  by 
which  any  theory  or  jiroposed  course  of  action  is  justi 
fied.  A  person  would  be  guilty  of  Division  if  he  should 
argue  that,  becatise  a  complex  theory  is  not  completely 
]")roved,  none  of  the  arguments  by  which  it  is  supported 
have  any  value.  It  is,  however,  j)erhaj)s  more  common 
to  fall  into  the  fallacy  of  Conij)osition  in  combating  the 
arguments  of  an  opponent.  Some  measiu'e,  for  example, 
is  proposed  to  which  a  person  finds  himself  in  oj)posi- 
tion.  It  is  usually  easy  to  analyze  the  different  argu- 
nunts  which  have  been  advanced  in  si'.pport  of  the 
measure,  and  to  show  that  no  single  one  of  these  I'u/if// 


I 


"I  a 

dentn 

expre 

<//(■///; 

Co/nu 
that 
accidi 
iKitun 
(I'f  (Hi 
\\ 


\ 


,  .11 


'   ,  \ 


p:vrls, 
rls  Lict 

f  Corn- 
true  ot 
finitely. 
coHoc- 
L>  minor 
pic  will 


Ics, 


cfits  the 
fit  every 
tance  of 
nijiles  of 
so  com- 
ments by 


IS    J  1 1  .^  i ' 


ie 


:  should 

ui)letely 
upported 

common 
atin^^  the 

cxami)U', 
n  oppt'si- 
cnt  ar^u- 
rt  of  the 
fccsc  /a/vi-n 


\ 


§46.     MATKklAI.    1AI.I.A(II:S 


1^'3 


/>]'  itself  is  sufficient  to  justify  the  change.  The  con- 
clusion may  then  be  drawn  with  a  fnic  show  of  logic 
that  all  the  reasons  advanced  have  been  insufficient. 
This,  of  course,  is  t*  neglect  the  cumulative  effect  of 
the  arguments;  it  is  to  assuriie  that  what  is  true  of 
'all,'  taken  distributively,  is  also  true  of  'all'  when 
taken    in    conjunction. 

(4)  It  is  often  difficult  to  distinguish  the  various  forms 
of  the  fallacy  of  Accident  from  Composition  and  Divi- 
sion. We  have  seen  that  the  latter  rest  upon  a  confu- 
sion between  whole  and  i)art;  or,  as  we  have  already 
expressed  it,  on  an  etpiivocation  between  the  distributive 
and  collective  use  of  terms.  'l"he  fallacies  of  Accident 
are  also  due  to  iMpiivocation.  Hut  in  this  case  the  con- 
fusion is  between  essential  properties  and  accidents, 
between  what  is  true  of  a  thing  in  its  real  tiature,  as 
expressed  by  its  logic:d  definition,  and  what  is  true  of  it 
only  under  some  peculiar  or  accidental  circumstance. 

There  are  two  forms  of  this  argument  which  arc 
usually  recognized:  {a)  The  Piirr/  or  Siiii/^li-  l^'allacy 
of  Accident,  which  consists  in  arguing  that  what  is  true 
of  a  thing  generally  is  also  true  of  it  under  some  acci- 
dental or  peculiar  circumstance.  The  old  lo  us 
exi)ressed  this  in  the  formula,  a  dicto  siuiplicu  <t<l 
dicluni  scrniiilinii  t/iiid.  The  second  foim  is  (  the 
Cotivtrsi-  Fallacy  of  Accident,  which  consists  in  :  ling 
that  what  is  true  of  a  thing  under  some  con^  .  ju  or 
accident,  can  be  asserted  of  it  simply,  or  in  its  essential 
nature.  The  formula  for  this  is,  a  dicto  siciindnv!  quid 
ad  dictiufi  situplicitcr. 

it   would   be    an    illustration  of  the  direct  fallacy  to 


t« 


i( 


'I  \ 


U89 


i     ! 


J! 


V    \ 


ii 


*     *• 


164 


r.M.I.ACIKS  OF   I)i:DUtTIVK   KKASoNINCi 


reason,  that  because  man  is  a  rational  bein^,  there- 
lore  a  drunken  man  or  an  an,L,ny  man  will  be  j^uided  by 
revson.  Similarly,  we  should  commit  this  fallacy  il 
we  were  to  ari;ue  t'uit  because  beefsteak  is  wholesome 
food,  it  would  be  j^ood  tor  a  person  sulTerin;;'  with  fever 
or  dysi)epsia  ;  or  to  conclude  Irom  the  pri!uij)le  that 
it  is  ri^lit  to  relieve  tiie  .sulTerin;^  ot  others,  that  we 
ouj;ht  to  <^ive  money  to  be<^|;ars. 

It  would  be  a  case  of  the  converse  f;dlacy  to  ar<;ue, 
that  because  si)irituous  liijuors  are  of  value  in  certain 
cases  of  disease,  they  must  therefore  be  beneficial  to  a 
person  who  is  well.  W'e  sliould  also  be  guilty  of  Ih^' 
same  fallacy  if  we  should  conclude  that  it  is  ri^ht  to 
deceive  others,  from  the  fact  that  it  is  sometimes  neces- 
sary to  keep  the  truth  froni  a  person  who  is  sick,  or  to 
deceive  an  enemy  in  time  of  war. 

The  fallacies  of  Accident,  like  all  the  fallacies  of 
Kquivo'-ation,  are  lar;;ely  the  result  of  a  loose  and  care- 
less use  of  lant;uai;e.  Hy  ([ualifyinj^  oin*  terms  so  as 
to  state  the  exact  circumstances  involved,  they  may 
casilv  be  detected   and   avoided. 

(/))  l^ailticics  of  Prcsuviptio)i.  —  The  fallacies  of  this 
grouj)  arc  the  result  of  ])resumi)tion  or  assumj)ti()n  on 
the  part  c^f  the  person  makini;  the  ar<;'ument.  It  is  i)os- 
sible  (i)  to  assume  the  point  to  be  [)roved,  either  in 
the  premises  of  an  argument,  or  in  a  (piestion  {Pctitio 
Principii,  and  Complex  Question);  or  (2)  to  assume 
without  warrant  that  a  certain  conclusion  follows  froni 
premises  which  have  been  stated  {Xoii  Siu]iiitur)\  01 
(3)  that  the  conclusion  obtained  proves  the  point  ;it 
issue  (Irrelevant  Conclusion). 


n 


§  46.     MATI.RIAI-    FAIJ-ACIKS 


165 


the  re- 
eled by 
lacy  ii' 
ilesomc 
1'.  fever 
)le  lliat 
:lKit  we 

)  ar^ue, 
certain 
ial  to  a 
y/  of  thr 
ri^ht  to 
•s  neces- 
:k,  or  to 


acies   ( 


)f 


lul  care- 

is  so  as 
ley   may 

of  this 
)tion  on 
I  is  pos- 
eilher  in 

( Pet  it  10 

assume 
tws  from 
itiir)\  <>!■ 

point  al 


\ 


''(i)  Prtitio  Principii,  or  '  I^c<;<j;in<;  the  Question,'  is  a 
form  of  arj^ument  whicii  assumes  the  concUision  to  be 
proved.  Tliis  may  be  done  in  either  of  two  ways, 
(i)  We  may  postulate  the  fact  which  we  wish  to  prove, 
or  its  ecjuivalent  under  another  name.  Thus,  for  ex- 
ample, we  miujht  ar<;ue  that  an  act  is  morally  wrong 
because  it  is  oj)i-)()scd  to  sound  ethical  principles.  'The 
soul  is  immortal  because  it  is  a  simple  and  indecom- 
|)osable  substance,'  may  be  regarded  as  another  ex- 
ample of  this  assumj)tion.  Hut  (2)  the  question  may 
be  begged  by  making  a  general  assumption  covering 
the  jjarticular  j)()int  in  dispute.  Thus,  if  the  advisa- 
bility of  legislation  regulating  the  hours  of  labor  in  a 
mine  or  factory  were  under  discussion,  the  cpiestion- 
begging  j)roposition,  '.all  legislation  which  interferes 
witli  the  right  of  free  contract  is  bad,'  n.'i.JU  be  pro- 
pounded as  a  settlement  of  the  whole  (j>'e.,tion, 

A  s|)eci:il  form  of  this  fallacy  results  when  each  of 
two  pro])ositions  is  used  in  turn  to  prove  the  truth  of 
the  '^ther.  This  is  known  as  *  reasoning  in  a  circle,' 
or  c'urulns  in  prohanJo.  This  method  of  reasoning  is 
nften  adopted  when  the  premise,  which  has  been  em- 
ployed to  prove  the  first  conclusion,  is  challenged.  '  I 
^houkl  not  do  this  act,  because  it  is  wrong.'  '  lint  how 
do  you  know  that  the  act  is  wrong  .^ '  *VVhy,  because 
I  know  that  I  should  not  do  it.' 

Ii  is  always  necessary,  then,  to  see  that  the  conclu- 
sion has  not  been  assumed  in  the  premises.  I^ut,  since 
the  conclusion  always  follows  friun  the  premises,  we 
may  say  in  one  sense  that  the- conclusion  is  always  thus 
assumed.     It  is,  therefore,  ea.sy  to  charge  an  opponent 


^1 


I    f 


Ij       m; 


i  : 

f 

t    1 

iS 

IAI.I,A(  IKS   (>!•    DKhl'CTIVK    K1;AS()NI\(; 


unjustly  with  he<;^inj;  the  cjucslion.  I)c  Morgan  in  his 
work  on  Fallacies,  says:  "There  is  an  opponent  fallacy 
to  the  Pctitio  Primipii  which,  I  suspect,  is  of  more 
frequent  occurrence :  it  is  the  habit  of  many  to  treat 
an  advanced  proposition  as  a  be<^^,i;ing  of  the  question 
the  moment  they  see  that,  if  established,  it  would  es- 
tablish the  question."  All  argument  must,  of  course, 
start  from  premises  to  which  both  parties  assent.  But 
candour  and  fairness  forbid  us  to  charge  an  opponent 
with  l\'titio  because  the  results  of  his  premises  are 
unwelcome.  It  was  C'harles  Lamb  who  humorously 
remarked  that  he  would  not  grant  that  two  and  two 
are  four  until  he  knew  what  use  was  to  be  made  of 
the  admission. 

(2)  The  Complex  Question  is  an  interrogative  form  of 
Pctitio.  It  is  not  really  a  simplex  interrogation,  but  is 
founded  upon  an  assumption.  Examples  may  be  found 
in  popular  pleasantries,  such  as,  '  Have  you  given  up 
your  drinking  habits } '  '  Do  the  j)eople  in  your  part  of 
tl  <  country  still  carry  revolvers,-' '  Disjunctive c[uestions, 
too,  always  contain  an  assumption  of  this  kind  :  *  Is  this 
an  oak  or  an  ash } '  *  Does  he  live  in  Boston  or 
New  York  ,'' '  The  '  leading  questions  '  which  lawyers 
frequently  use  in  examining  witnesses,  but  which  are 
always  objected  to  by  the  opposing  counsel,  are  usually 
of  this  character.  Further  instances  may  perhaps  be 
found  in  the  demand  for  explanation  of  facts  which  are 
either  false,  or  not  fully  substantiated;  as,  e.g.  'Why 
does  a  fish  when  dead  weigh  more  than  when  alive } ' 
'  What  is  the  explanation  of  mind-reading  .-^ ' 

(3)  The   IrrCievant   Conclusion,  or   Ignomtio   El  cue  Id, 


§46.     MATEKIAI.    lAI.LACIKS 


{(')•/ 


1  in  his 
fiilUicy 
f   more 
o  trout 
ucstion 
)uld  es- 
course, 
t.     But 
oponcnt 
Iscs  arc 
lorously 
ind  two 
iiaclc  of 

form  of 
n,  Init  is 
)c  found 
!;ivcn  up 
part  of 
uostions, 
'  Is  this 
ston   or 
lawyers 
lich  arc 
usually 
haps  be 
hich  arc 
.'-.  'Why 
1  alive  ? ' 

Ehnchi, 


consists  in  substituting  for  the  coiU'liision  to  be  proved 
some  other  proposition  more  or  less  nearly  related  to  it. 
This  fallacy  may  oe  the  result  of  an  involuntary  con- 
fusion on  the  part  of  the  person  employing  it.  or  it  may 
be  consciously  adopted  as  a  controversial  stratagem  to 
deceive  an  (opponent  or  an  audience.  When  used  in 
this  latter  way,  it  is  usually  intended  to  conceal  the 
weakness  of  a  position  by  diverting  attention  from  the 
real  point  at  issue.  This  is,  indeed,  a  favourite  device 
of  those  who  have  to  support  a  weak  case.  A  counsel 
for  the  defence  in  a  law-suit  is  said  to  have  handed 
to  the  barrister  presenting  the  case  the  brief  marked, 
'No  case;  abuse  the  plaintiff's  attorney.'  To  answer 
a  charge  or  accusation  by  declaring  that  the  person 
bringing  the  charge  is  guilty  of  as  bad,  or  even  worse, 
things,  —  what  is  sometimes  called  the  ///  qiioqitc  form 
of  argument  —  is  also  an  example  of  this  fallacy. 

Apart  from  such  wilful  perversions  or  (^on fusions, 
many  unintentional  instances  of  this  fallacy  occur.  In 
controversial  writing,  it  is  very  natural  to  assume  that 
a  proposition  which  has  some  points  of  connection  with 
the  conclusion  to  be  established,  is  '  essentially  the 
same  thing,'  or  *  practically  the  same,  as  the  thesis 
maintained.'  Thus  one  might  take  the  fact  that  a  great 
many  people  are  not  regular  church-goers,  as  a  proof 
of  the  proposition  that  religion  and  morality  are  dying- 
out  in  the  country.  Many  of  the  arguments  brought 
against  scientific  and  philosophical  theories  belong  to 
this  class.  Mill  cites  the  arguments  which  have  been 
urged  against  the  Malthusian  doctrine  of  population, 
and  Berkeley's  theory  of  matter.     We  may  quote  the 


' ,    I 


1 68 


lAI.l.ACIKS   OK   DLiDUCriVI-:   KliASOMNG 


passaj:;e  rolcniii};  lo  llio  lormcr:  "  Maltluis  luis  been 
supposed  ti>  l)c  refuted  it  it  could  l)e  shown  that  in 
some  countries  or  a«;es  |)oj)ulation  has  been  nearly 
stationary,  [is  if  he  had  asserted  that  population  always 
increases  in  a  j^iven  ratio,  or  had  not  expressly  declared 
that  it  increases  only,  in  so  far  as  it  is  not  restrained  by 
prudence,  or  kept  down  by  disease.  Or,  i)erhaj)s,  a 
collection  of  facts  is  |)roduced  to  prove  that  in  some  one 
country  with  a  dense  population  the  people  are  better 
off  than  they  are  in  another  country  with  a  thin  one,  or 
that  the  people  have  become  better  off  and  more 
nun^erous  at  the  same  time;  as  if  the  assertion  were 
that  a  dense  ))()j)ulation  could  not  i)ossibly  1)e  well  off."  ' 

There  are  several  cases  or  forms  of  Irrelevant  Con- 
clusion to  whicli  special  names  have  been  given,  and 
which  it  is  important  to  consider  separately.  VV'ien 
an  argument  bears  uj^on  the  real  point  at  issue,  it  is 
called  an^itmciitiiii;  ad  irvi.  Hut,  on  the  other  hand, 
there  are  the  following  special  ways  of  obsciu'ing  the 
issue  :  — argiivicntuni  nd  liouiiiuiH,  ai'<^/u>nntinii  lui  popn- 
lum,  ari^nincntiitii  ad  ignonintiai)iy  and  argnifnut/un  ad 
vcrccHudiam. 

The  argimicntiim  ad  Jiomincm  is  an  a]-)j)eal  to  the 
character,  ju-inciples,  or  former  profession  of  the  i)erson 
against  whom  it  is  directed.  It  has  reference  to  a 
person  or  persons,  not  to  the  real  matter  under  discus- 
sion. In  order  to  confuse  an  opponent,  and  discredit 
him  with  the  audience,  one  may  show  that  his  charactei 
is  bad,  or  that  the  views  which  he  is  now  maintaining 

i/.^i,'/V,  Uk.  V.  Cli.  VII.  §3. 


I 


The 

str:ir 
impo.'^ 
wo  h:i 
those 


■v,: 


§4f'.     MAIKklAI,    lAI.I.AClES 


169 


.    H"' 


f      *' 


;  been 
bul  in 

nearly 
always 
jelared 
necl  by 
iai)s,  a 
mc  one 
:  better 

one,  or 

I  more 
)n  were 

II  off."  » 
mt  Con- 
•en,  and 

W'len 
ue,  it  is 
ir  band, 
•ni^  the 
jd  popu- 
jitiDU  ad 

to  the 
c  ])erson 
ice  to  a 
r  discus- 
discredit 
haractei 
ntainin;; 


are  inconsistent  with  bis  fonnei'  j)H)fessi()ns  add  practice. 
C)r  tbe  arj^umenl  may  be  nsed  willi  the  liope  of  persnad- 
ini;  the  opponent  himself.  We  then  try  to  convince 
him  that  the  position  wliich  he  maintains  is  inconsistent 
with  some  other  view  whicii  lie  has  i)rcviously  pro- 
fessed, or  with  the  principles  of  some  sect  or  party 
which  he  has  approved.  Or  we  may  ai)peal  to  his  in- 
terests by  showing  him  that  the  action  proposed  will 
affect  injuriously  some  cause  in  which  he  is  concerned, 
or  will  benefit  .some  rival  sect  or  party.  In  all  of  these 
cases  the  real  point  at  issue  is,  of  course,  evaded. 

The  aJxmficNtnin  ad  topithim  is  an  argument  ad- 
dressed to  the  feclin.i;s,  passions,  and  prejudices  of 
j)eoj)le  ratiier  tiian  .m  unbias.sed  di.scussion  addressed  to 
the  intellect. 

The  nixinunitiun  ad  ii^.wvantiaw  is  an  attemj-jt  to 
^ain  su|)port  for  some  position  by  dwellini;-  upon  the 
imi)ossibility  of  i)rovini;"  the  opposite.  'I'iuis  we  cannot 
prove  affirmatively  that  spirits  do  not  revisit  the  earth, 
or  send  messai^es  to  former  friends  throui;h  'mediums.' 
Now  it  is  not  unusual  to  find  ii^norance  on  this  subject 
advanced  as  a  j)ositive  ground  of  conviction.  The 
ar,L;ument   seems  to  be  :  — 

It  is  not  inipossihlo  tliat  this  is  so, 
Wlv  t  is  iu)t  impossihle  is  possible, 
Tlu-icforo  it  is  possible  that  this  is  so. 

The  fallacy  arises  when  we  confuse  what  is  only  ab- 
stractly jiossible  /.<•.,  what  we  cannot  prove  to  be 
impossible  —  with  what  is  really  i)ossible,  '".r.,  with  what 
we  have  souic  positive  LCrounds  for  1)elievin<^  in,  thou<^h 
those  grounds  are  not  sufficiiMit  to  produce  coiivirtion. 


r 


C' 


^ij 


r  "'^ 


i;'i 


'I  1 


hi 


r  ( 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


I.I 


11.25 


(3  0      "^ 

!:  1^   12.0 


IM 

2.2 


U    11 1.6 


i 


.^t' 


Photographic 

Sciences 
Corporation 


{^ 


k\ 


«- 


-"\ 


^9> 


V 


23  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  872-4S03 


^ 
% 


o^ 


'1.^^^  <^ 


r 

O 


I/O 


FALLACIES   OF   DEDUCTIVE   REASONING 


,  I 


|i  .) 


!i 


■I         ! 


The  arguniciituui  ad  vcrcciindiani  is  an  appeal  to  the 
reverence  which  most  people  feel  for  a  great  name. 
This  method  of  reasoning  attempts  to  settle  a  question 
by  referring  to  the  opinion  of  some  acknowledged 
authority,  without  any  consideration  of  the  arguments 
which  are  advanced  for  or  against  the  position.  It  is,  of 
course,  right  to  attach  much  importance  to  the  views  of 
great  men,  but  we  must  not  suppose  that  their  opinion 
amounts  to  proof,  or  forbids  us  to  consider  the  matter 
for  ourselves. 

There  is,  however,  a  more  common,  though  still  less 
justifiable,  form  of  the  argument  from  authority.  A 
man  who  is  distinguished  for  his  knowledge  and  attain- 
ments in  some  particular  field,  is  often  quoted  as  an 
authority  upon  questions  with  which  he  has  no  special 
acquaintance.  The  prestige  of  a  great  name  is  thus 
irrelevantly  invoked  when  no  significance  properly 
attaches  to  it.  Thus,  for  example,  a  successful  general 
is  supposed  to  speak  with  authority  upon  problems  of 
statescraft,  and  the  opinions  of  prominent  clergymen 
are  quoted  regarding  the  latest  scientific  theories. 

(4)  The  fallacy  of  non  sequitur,  or  tJic  fallacy  of  the 
consequent,  occurs  when  the  conclusion  does  not  really 
follow  from  the  premises  by  which  it  is  supposed  to  be 
supported.  The  following  example  may  serve  as  an 
illustration  :  — 

Pennsyh-ania  contains  rich  coal  and  iron  mines, 
Pennsylvania  has  no  sea-coast, 


Therefore  the  battle  of  Gettysburg  was  fought  in  that  state. 
This  argument,  of  course,  is  thoroughly  inconsequent, 


to  the 

name, 
aestion 
'ledged 
uments 
It  is,  of 
lews  of 
opinion 
;  matter 

jtill  less 
rity.  A 
i  attain- 
d  as  an 
)  special 
;  is  thus 
properly 

general 
blems  of 

^rgymen 

s. 

f)/  of  the 

|ot  really 

,cd  to  be 

e  as  an 


state, 
isequent, 


§46.     MATERIAL    lALLACIKS 


171 


and  would  deceive  no  one.  But  when  the  conclusion 
repeats  some  words  or  phrases  from  the  premises,  we 
are  likely,  when  not  j)aying  close  attention,  to  be  im- 
posed upon  by  the  mere  form  of  the  argument.  We 
notice  the  premises,  and  remark  that  the  person  using 
the  argument  advances  boldly  through  '  therefore  '  to  his 
conclusion.  And  if  this  conclusion  ai)pears  to  be  related 
to  the  premises,  and  sounds  reasonable,  the  argument  is 
likely  to  be  accepted.  The  following  example  will  illus- 
trate this :  — 

Every  one  desires  happiness,  and  virtuous  people  are  happy, 
Therefore  every  one  desires  to  be  virtuous. 

What  is  known  as  the  False  Cause  {non  causa  pro 
causa  ;  post  Jioc  ergo  propter  hoc)  is  the  inductive  fallacy 
corresponding  to  the  non  scquitur.  In  this  \\  .ssume 
that  one  thing  is  the  cause  of  another  merely  because  we 
have  known  them  to  happen  together  a  number  of  times. 
The  causal  relation  is  assumed  without  any  analysis  or 
examination,  on  the  ground  of  some  chance  coincidence. 
Thus  a  change  in  the  weather  may  be  attributed  to  the 
moon,  or  the  prosperity  of  the  country  to  its  laws  re- 
quiring Sunday  observance  (cf.  pp.  255  f.). 

References 

J.  H.  Hyslop,  The  Eletnents  of  Logic,  Chs.  XVII.  and  XVIII. 

J.  S.  l,\\\\.  Logic,  1 5k.  V. 

A.  Sidgwick,  Fallacies  [Int.  Scient.  Series]. 


I     111 


'(    1 


i> 


iii:l 


- 


' 

! 

fi 

1 

i     . 

I 

1    ■: 

I  1 

V:i. 

■■ 

( 

i    ■' 

PART    II.— INDUCTIVE    METHODS 


CHAPTER   XIII 


THE    PROBLEM    OF    INDUCTION.       OBSERVATION    AND 

EXPLANATION 

§  47.  The  Problem  of  Induction.  —  In  Part  I.  wc  have 
outlined  the  general  nature  of  the  syllogism,  and  have 
shown  what  conditions  must  be  fulfilled  in  order  to 
derive  valid  conclusions  from  given  premises..  But  the 
syllogism  does  not  represent  completely  all  of  our  ways  of 
thinking.  We  do  not  always  find  premises  which  every 
one  accepts  ready  to  our  hand.  The  propositions  which 
serve  as  the  premises  of  syllogisms  are  themselves  the 
result  of  the  activity  of  thought.  It  requires  thinking 
to  arrive  at  such  simple  propositions  as,  '  all  men  arc 
mortal,'  *  water  is  composed  of  hydrogen  and  oxygen.' 
F'acts  of  this  kind  are  of  course  learned  through  expe- 
rience, but  they  none  the  less  require  thought  for  thgir 
discovery.  Sense-perception  without  thought  could  give 
us  only  a  chaos  of  unordered  impressions  which  would 
have  no  meaning  and  no  significance.  It  is  important, 
then,  to  understand  how  our  intelligence  proceeds  to 
discover  the  real  nature  of  things,  and  the  laws  accord- 
ing to  which  they  operate.  Thinking  is  the  means  by 
which  we  interpret  nature,  and  to  show  how  this  is  to 

172 


DS 


AND 

vc  have 
id  have 
irder  to 
But  the 
ways  of 
h  every 
s  which 
ves  the 
1  hi  king 
icn  are 
)xygcn.' 
;h  expe- 
nr  thgir 
.lid  give 
would 
lortant, 
eeds  to 
accord- 
ans  by 
is  is  to 


§47.     THE   PKOBLEM   OF   INDUCTION 


173 


be  accompHshed  was  the  purpose  of  Bacon's  Novum  Or- 
gaiuint.  The  problem  is  the  discovery  of  the  real  nature 
of  things,  and  their  relations  with  one  another.  The 
assumption  of  all  knowledge,  as  we  have  already  seen 
(§  9,  cf.  also  §§  79,  80),  is  that  there  is  a  permanent  con- 
stitution cf  things  which  secures  uniform  ways  of  acting. 
The  procedure  by  means  of  which  intelligence  discovers 
the  permanent  laws  of  things  is  usually  known  as  \n- 
duction.  We  shall  have  to  study  this  kind  of  thinking 
in  this  and  the  following  chapters.  The  general  prob- 
lem may  perhaps  be  stated  in  this  way :  What  are  the 
methods  which  inductive  thinking  employs,  in  order  to 
pass  from  the  chaotic  and  unordered  form  in  which  the 
senses  present  our  experience,  to  a  perception  of  the 
order  and  law  in  things  that  is  required  by  real  know- 
ledge or  science  ? 

Before  we  attempt  to  answer  this  question,  however, 
there  are  several  remarks  to  be  made  which  will,  I 
hope,  throw  further  light  upon  the  nature  of  our  under- 
taking. In  the  first  place,  it  is  to  be  noticed  that  we 
have  spoken  in  the  preceding  paragraph  of  the  methods 
of  inductive  thinking.  Now,  as  we  shall  show  more 
fully  in  §  d,^,  there  is  no  essential  difference  between 
the  res  Jilts  of  an  inductive  and  a  deductive  inference. 
The  purpose  of  an  inference  is  always  the  same; 
namely,  to  exhibit  the  relation  and  connection  of  par- 
ticular facts  or  events,  in  virtue  of  some  universal  law 
or  principle.  In  deductive  thinking,  such  a  law  is 
known,  or  provisionally  assumed  as  known,  and  the 
problem  is  to  show  its  application  to  the  facts  with 
which  we  are  dealing.     In  induction,  on  the  other  hand, 


1s|ilS  I 


.If' 
I 


'  ti ' 


H 


<. 


'I   "^ 


1    ■  V  M 


1 


n    si 


i:i, 


't 


n; 


cask  wnicn  tnouf^nt  has  to  pcrrorm  is  to  discover  tiic 
general  law  of  their  connection.  15oth  deduction  and 
induction  play  an  important  part  in  the  work  of  building 
up  knowledge.  ]5ut  the  various  sciences  must  start 
with  particular  facts  learned  through  experience.  The 
mind  has  not  before  exi)erience  any  store  of  general 
principles  or  innate  truths  which  might  serve  as  the 
starting-point  of  knowledge  (cf.  §  76).  It  must  fall 
back,  therefore,  upon  the  particular  facts  and  events 
learned  through  perception.  This  'elementary  know- 
ledge,' as  has  been  already  pointed  out,  does  not  pass 
over  in  a  ready-made  form  into  the  mind,  but  is  itself 
the  result  of  thinking  or  judging.  However,  before 
any  one  deliberately  and  consciously  undertakes  to  dis- 
cover new  truth,  to  understand  the  world,  he  is  already 
in  possession  of  a  store  of  such  perceptive  judgments. 
These  constitute  the  beginnings  of  knowledge,  and 
serve  as  the  starting-point  for  scientific  explanation. 
The  knowledge  of  laws  and  general  principles  comc^ 
l^ter,  and  is  derived  from  a  study  of  the  particular_fagts^ 
It  is  clear,  then,  that  the  procedure  of  all  the  sciences 
must  be  inductive,  at  least  in  the  beginning.  The  various 
sciences  are  occupied,  each  in  its  particular  field,  with 
an  attempt  to  reduce  to  order  and  unity  facts,  which  at 
first  sight  appear  to  be  lawless  and  disconnected.  And 
it  is  true  to  say  that  in  this  undertaking  the  general 
procedure  is  inductive.  But  it  will  also  appear  that  in 
performing  this  task  thought  does  not  always  proceed 
in  strictly  inductive  fashion.  Our  thought  uses  every 
means  which  will  heli:)  it  to  its  desired  end.     It  is  often 


I 


8  47- 


TIIK   rkOULKM   ol'   INDUCTION 


175 


id  the 
er  the 
n  and 
lilding 
t   start 
The 
jeneral 
as  the 
1st  fall 
events 
know- 
ot  pass 
is  itself 
before 
to  dis- 
1  already 
[rments. 


o;cneral 
that  in 
)roceed 
:s  every 
IS  often 


able,  after  pushing  its  inc|uines  a  little  way,  to  discover 
some  general  principle,  or  to  guess  what  the  law  of 
connection  must  be.  When  this  is  possible,  it  is  found 
profitable  to  proceed  deductively,  and  to  show  what  re- 
sults necessarily  follow  from  the  truth  of  such  a  general 
law.  Of  course,  it  is  always  essential  to  verify  results 
obtained  in  this  deductive  way,  by  comparing  them  with 
the  actual  facts.  But  in  general,  the  best  results  are 
obtained  when  induction  and  deduction  go  hand  in 
hand.  We  shall  expect  to  find,  then,  that  the  so-called 
inductive  metliods  sometimes  include  steps  which  are 
really  deductive  in  nature. 

It  is  to  be  noticed,  further,  that  in  dc.iliiig  with  tlie  nature  of  the 
inductive  methods.  \vc  arc  not  laying  down  rules  which  thought  must 
follow.  We  are  not  attempting,  that  is,  \o  prvscrii'c  to  tliinking  its 
mode  of  procedure.  To  do  so  would  be  quite  futile.  It  is  impos- 
sible, as  we  have  already  seen  (§  3),  for  logic  to  lay  down  any 
a  priori  xwXq?,.  Its  task  is  rather  to  point  out  the  methods  by  which 
success  has  been  already  won  in  the  \arious  fields  of  knowledge. 
Logic  does  not  attempt  to  iirooit  any  methods  of  scientific  proced- 
ure, but  it  undertakes  to  describe  the  road  by  which  truth  has 
already  been  gained.  The  scientific  inquirer  is  interested  pri- 
marily in  the  results  of  his  thinking:  he  is  usually  not  interested  in 
tracing  the  various  steps  through  which  his  thought  has  passed,  and 
the  methods  employed  in  reaching  the  goal.  Oftentimes  he  would 
be  unable  to  give  any  such  description  even  if  he  tried  to  do  so. 
Logic,  however,  takes  the  procedure  of  the  thinking  process  for  its 
subject-matter.  It  undertakes  to  make  thought  conscious  of  its 
own  nature,  of  the  goal  at  which  it  aims,  and  the  methods  which 
are  employed  in  the  attainment  of  this  goal.  The  comparative 
value  of  these  methods,  too,  must  be  decided  by  the  actual  charac- 
ter of  the  results  which  they  have  yielded.  One  method  is  to  be 
regarded  as  better  than  another  when  it  gives  us  knowledge  which 
is  universally  acknowledged  to  be  more  complete  and  satisfactory 


-y 


'^ 


c 


■4 


1  : 

vi 

Wf 


iMi' 


■  r 


176 


THE   PRUULLM   OF   INDUCTION 


tluiii  that  alfordcd  hy  tlic  other.     Ikit  loijical  methods,  like  cvcry- 
thinjr  else,  must  he  known  and  judged  hy  their  fruits. 

Ajj^ain,  it  must  be  remembered  that  complete  scien- 
tific explanation,  which  we  found  to  be  the  type  of  per- 
fect knowledge,  is  not  attained  at  a  single  stroke. 
Scientific  inquiry  may  have  various  purposes.  It  is 
often  limited  to  an  attempt  to  gain  a  knowledge  of  the 
quantitative  relations  of  things,  or  of  the  way  in  which 
they  are  connected  as  antecedents  and  consequents. 
In  some  cases,  too,  the  conclusions  reached  are  only 
more  or  less  probable,  and  require  further  confirmation 
through  the  use  of  other  methods.  It  follows,  then, 
that  the  various  scientific  methods  which  we  shall  have 
to  describe  are  not  to  be  regarded  as  self-sufficient  and 
independent  ways  of  reaching  truth,  but  rather  as 
mutually  helpful  and  complementary.  For  example, 
the  work  done  by  thought  in  dealing  with  the  quantita- 
tive aspect  of  things,  and  the  conclusions  which  it 
reaches  through  analogical  inference,  are  necessary 
steps  in  the  progress  toward  complete  and  satisfactory 
explanations  of  the  nature  of  things.  We  shall  find  it 
necessar},  therefore,  to  keep  this  relation  of  the  various 
methods  to  one  another  in  mind  in  our  investigation. 
For  our  purpose,  we  may  perhaps  classify  the  various 
scientific  methods  as  Observation,  Analogy,  and  Com- 
plete Scientific  Explanation. 

§  48.  Observation. — We  may  include  under  this  head- 
ing. Simple  Enu7}ieratio}i,  Statistical  Methods,  and 
Methods  of  determining  Causal  Connection.  Before 
describing  these  processes  in  detail,  however,  it  is  neces- 


I  1 


A 


1,^ 


;  cvcry- 

scicn- 
li  pcr- 
strokc. 
It   is 
of  the 
which 
quents. 
e  only 
•mation 
5,  then, 
.11  have 
;nt  and 
:her    as 
xamplc, 
uantita- 
hich   it 
ccssary 
factory 
find  it 
various 
ligation, 
various 
x\  Com- 


iis  hcad- 
ds,  and 
Before 
is  neces- 


§48.    OnsKRVATION 


177 


sary  to  make  clear  what  is  impHed  in  the  naturr  of  scien- 
tific observation,  and  what  are  the  results  aimed  at  by  the 
methods  which  it  employs.  It  is  customary  to  say  that 
Observation  has  to  determine  the  nature  and  order  ot  the  - 
particular  facts  presented  by  our  experience,  and  that 
after  this  has  been  done,  there  still  remains  the  task  of 
furnishing  the  theory,  or  Explanation  of  the  facts.  This 
distinction,  though  not  absolute,  affords  a  convenient 
jirinciple  of  division  in  treating  of  the  inductive  methods. 
We  may  say  that  it  is  observation  which  enables  us  to  .y^ 
discover  the  nature  of  particular  facts,  and  to  determine 
the  order  of  their  connection.  Accurate  observation  is 
thus  a  first  and  necessary  step  in  the  work  of  reducing 
our  experience  to  systematic  form.  We  have  already 
seen  how  emphatically  and  eloquently  this  doctrine  was 
proclaimed  by  Bacon  in  the  Noviiiu  Organuni. 

It  is  important,  however,  to  remember  that  scientific 
observation  itself  involves  intellectual  activity.  To 
observe  —  at  least  in  the  sense  in  which  the  word  is 
used  in  scientific  procedure  —  requires  something  more 
than  the  passive  reception  of  impressions  of  sense  in 
the  order  in  which  they  come  to  us.  Without  some 
activity  on  the  part  of  mind,  it  would  be  impossible  to 
obtain  even  the  imperfect  and  fragmentary  knowledge 
of  everyday  life.  But  accurate  observation  is  one  of 
the  means  which  science  employs  to  render  this  know- 
ledge more  complete  and  satisfactory ;  and  when  obser- 
vation thus  becomes  an  exact.and  conscious  instrument, 
it  involves,  to  even  a  greater  extent  than  in  ordinary 
life,  intellectual  activities  like  jui]4iJllc;iL-aiid...i>rf€rcnce. 
It  is  because  this  is  true,  because  scientific  observation 

N 


u^ 


\m\ 


'.     "S 


»■! 


.'   i. 


\ 

1 

;        1 

1 
/ 

\ 

r  / 

^1 


-I 


i 


I   I    » 


If  11 


178 


niK    TKOULKM   Ol'    INDUCTION 


demands  the  constant  exercise  of  thou<j;ht,  in  selecting; 
and  comparin<;  the  various  elements  in  the  material 
with  which  it  deals,  that  it  affords  such  excellent  intel- 
lectual discipline.  The  observational  sciences  do  not 
merely  train  the  sense-organs;  the  discipline  which 
they  afford  is  mental  as  well  as  physiological,  and  it 
is,  of  course,  true  that  mental  trainin<;  can  only  be 
gained  through  the  exercise  of  mental  activity. 

It  is  quite  true  that  it  is  of  the  utmost  importance  to  dlstin^ruish 
between  a  fact,  and  further  inferences  from  the  fact.  As  will  be 
pointed  out  in  the  chapter  on  Inducti\e  Fallacies,  errors  very  fre- 
quently arise  from  confusing  facts  and  inferences.  Tlie  point  wliicli 
is  emphasized  in  the  previous  paragraph,  however,  is  that  it  requires 
a  certain  amount  of  tJiinkiuo;  in  order  to  get  a  fact  at  all.  Facts  do 
not  pass  over  ready-made  into  the  mind.  Simply  to  stare  at  things 
does  not  give  us  knowledge  ;  unless  our  mind  reacts,  judges,  thinks. 
we  are  not  a  bit  the  wiser  for  staring.  To  observe  well,  it  is  neces- 
sary to  be  more  or  less  definitely  conscious  of  what  one  is  looking 
for,  to  direct  one's  attention  towards  some  particular  field  or  object ; 
and  to  do  this  implies  selection  among  the  multitude  of  impressions 
and  objects  of  which  we  are  conscious.  Moreover,  scientific  obser- 
vation requires  analysis  and  discrimination.  It  is  not  unusual,  in 
text-books  on  logic,  to  symbolize  the  various  facts  learned  through 
observation  by  means  of  letters,  a^  b,  c,  etc.,  and  to  take  it  for  granted 
that  they  are  given  in  our  experience  as  distinct  and  separate  phe- 
nomena ;  but,  as  we  have  just  seen,  judgments  of  analysis  and 
discrimination  are  necessary  to  separate  out  the  so-called  'phenom- 
ena' from  the  mass  or  tangle  of  experience  in  which  they  were 
originally  given.  Again,  to  determine  the  nature  of  a  fact  through 
observation,  it  is  essential  to  note  carefully  how  it  differs  from 
other  facts  with  which  it  is  likely  to  be  confused,  and  also,  to  some 
extent,  what  relations  and  resemblances  it  has.  But  such  knowledge 
presupposes  tliat  thought  has  already  been  at  work  in  forming  judg- 
ments of  comparison. 


'■•S&. 


§  4''>-     ol'.SKRVAI'lON 


179 


cctint; 
atcruil 
L  intcl- 
do  not 
wiiich 
[ind  it 
nly   be 


stinj^uish 
s  will  be 
\L'i-y  fre- 
int  which 
t  ix'([uirt's 
I'acts  do 
at  thin^^s 
s.  thinks, 
is  ncces- 
s  looking 
)r  object ; 
ipressions 
ific  obscr- 
nusuah  in 
through 
.)!•  granted 
irate  phe- 
ysis   and 
phenom- 
they  were 
t  through 
ft'ers  from 
0,  to  some 
mowledge 
ning  judg- 


It  may  sec  .1  stranj;c  at  lirst  si,L;ht  tluit  the  determina- 
tion of  the  causal  order  and  connection  of  plienomena 
shoidd  be  regarded  as  belon;;ini;'  to  Observation  rather 
than  to  Explanation.     To  discover  the  causes  of  thin<;s 
is,  indeed,  a  very  essential  ste[)  in  the  process  of  expla- 
nation;    but,  as  will   appear   more   fidly  hereafter,  the 
distinction  between  observation  and  explanation  is  not 
an  absolute  one.     The  process  of  kn()wledj;"e  is  essen- 
tially the  same  from  be[;innin<.^  to  end.     The  determina- 
tion of  the  nature  and  order  of  phenomena  is  a  long 
step  towards  rendering  them   comprehensible.     If  the 
distinction   between    observation    and    explanation     as 
methods  of  scientific  procedure  is  to  be  made,  it  seems 
right  to  assign  to  observation  the  task  of  determining 
what  phenomena  are  invariably  conjoined  as  antecedents 
and  consequents.      Experience  ])rcsents  to  us  a  variety 
of  objects  simultaneously   or  in   rapid   succession,  but 
in  many  cases   such   conjunction   is  merely  temporary 
and   accidental.      The   problem  which   scientific  obser-  ^ 
'  vation  has  here  to  determine  is  the  discovery  of  what 
particular  phenomena  are  Jirccssari/y  connected,  what  are 
the  real  antecedents  and  consequents  in  the  case.    'The 
sun  was  very  hot  this  morning,  and  a  picnic  party  went 
on  the  lake,  and  this  afternoon  there  is  a  severe  thunder- 
storm.'    These  events  (and  many  others)  are  conjoined 
temporally.     Is  there   also  a  real   connection   between 
any  of  them,  or  is  their  concurrence  merely  accidental  .<* 
This  is  the  question  which   must  be  answered  by  the 
methods  of  determining  causal  connection.     Of  course 
merely  passive  observation  will  not  suffice  to  obtain  an 
answer.     The  relation  of  antecedent  and  consequent  is 


■'  'I 
i.  bil 

'1  ^ 


'\  t 


1i';.r 


.<.l 


mm 


,    i' 


I      I 


180 


TIIK    I'KOIM.IM    <)!•    INDl'C^rioX 


not  i^iviii,  but  lias  to  be  made  out  l)y  the  help  of  analysis 
and  inlcronce.  Hut,  since  tin*  point  to  he  deteiniincd 
has  rclcrcncc  to  the  nature  and  order  ol  a  set  ol  facts 
which  can  be  observed,  the  methods  employed  may  well 
be  included  under  Observation. 

A  tlistinetion  is  sometiuies  made  between  observa- 
tion and  experinuiil.  In  observation,  it  is  said,  the 
mind  simply  ////^/.v  its  results  presented  to  it  in  nature, 
while  in  experiment  the  answer  to  a  cpiestion  is  obtained 
by  actively  controlliuL;  and  arrani;in.i;"  the  circumstances 
at  will.  There  is,  no  doubt,  some  grounds  for  this  dis- 
tinction, thoui;h  it  is  not  true  that  the  mind  is  passive 
in  the  one  case,  and  active  in  the  other.  l*Aen  in  ob- 
servation, as  we  have  seen,  knowledi^e  always  arises 
thr()U<;"h  active  analysis  and  comparison  of  the  impres- 
sions received  through  sense.  The  difference  is  rather 
this:  In  observing,  where  experiment  is  impossible,  one 
must  wait  for  events  to  occur,  and  must  take  them  in 
the  order  in  which  they  are  presented  in  the  natural 
series.  JUit,  where  experiment  is  employed,  we  have 
control  of  the  conditions,  and  can  produce  the  phe- 
nomena to  be  investigated  in  any  order,  and  as  often 
as  we  choose.  In  experiment,  as  Bacon  says,  we  can 
put  definite  questions  to  nature,  and  compel  her  to 
answer.  This  is,  of  course,  an  immense  advantage. 
In  some  of  the  sciences,  however  —  geology  and  as- 
tronomy for  example  —  it  is  not  possible  thus  to  con- 
trol the  conditions :  one  must  wait  and  observe  the 
results  of  nature's  experiments.  Physics  and  chemis- 
try arc  the  experimental  sciences  par  excellence ;  and, 
in  general,  we  may  say  that  a  science  always  makes 


§.}S.    ollSKkVATIoN 


iSi 


more  r:i|)i(l  progress  wlu-n  it  is  Iniiiul  jxissihK'  to  call 
cxpciiinciit  to  tlic  aid  ol  observation.  It  is  not  jxissihlc 
to  conceive  how  physics  and  clieinistry  could  have 
reached  their  i)resent  stale  of  pcrtection  without  the 
assistance  of  exiieriment.  Indeed,  the  almost  total 
neglect  of  experiment  by  the  (iieek  and  mediirval 
scholars  must  be  reL;arde(l  as  one  of  the  chief  reasons 
why  the  physical  sciences  made  so  little  i)ro^ress  dur- 
ing;' those  centuries.  Dr.  I^\)wler  states  in  the  following 
j)assa<^c  some  of  the  main  advantages  to  be  derived 
from  experiment:  — 

"To  l)c  ;il)lt.'  to  vary  the  circunistatices  as  we  clioose,  to  produce 
the  phenomenon  under  investi.i^ation  in  the  precise  de;^ree  which  is 
most  convenient  to  us.  and  as  fre(|uently  as  we  wisli,  to  combine  it 
with  (jther  phenomena  or  to  isolate  it  altot^ether.  are  such  ohvious 
advanta,i;cs  that  it  Is  not  necessary  to  insist  upon  them.  Without 
the  aid  of  artificial  experiment  it  wouhl  ha\e  been  impossible,  for 
instance,  to  ascertain  the  laws  of  fallintj  i)odies.  To  (Hsprove  the 
old  theory  that  bitdies  fall  in  times  inversely  proportioned  to  their 
weight,  it  was  necessary  to  try  the  ex|)eriment ;  to  i)c  al)lt'  to  affirm 
with  certainty  that  .ill  bodies,  if  movini,^  in  a  non-resisting  m(;diimi. 
would  fall  to  the  earth  through  e(|ual  vertical  spaces  in  ecpial  times, 
it  was  essential  to  possess  tlie  means  of  removiu';-  altotjether  the 
resistin;^;  medium  by  some  such  contrivance  as  that  of  the  air-i)ump. 
.  .  .  I'Lven  when  observation  alone  reveals  to  us  a  fact  of  nature, 
experiment  is  often  necessary  in  order  to  j^ivc  precision  to  our 
knowledge.  That  the  metals  are  fusible,  and  that  some  are  fusi])le 
at  a  lower  temperature  than  others,  is  a  fact  which  we  can  conceive 
to  have  been  obtruded  upon  man's  observation,  I)ul  the  ])recise 
temperature  at  which  each  metal  be,2;ins  to  chaui^e  the  solid  for  the 
li{|uid  condition  could  be  learned  only  by  artificial  experiment."  ^ 

It  is  important,  then,  to  recognize  the  services  which 

•  Fowler,  [nductive  Lo^i^ic,  p.  41  f. 


"1 


«.    It 


) 


fmmsmm 


V 


I 

•  ! 


! 


Ml 


1'  m 


V, 

1, 1i 


^ 


182 


TIIK    rR015LEM   OF    INDUCTION 


experiment  renders  in  helping  us  to  understand  the 
facts  with  which  the  various  sciences  deal.  But  it  is  not 
necessary  to  distinguish  experiment  from  ohservation  as 
if  it  were  a  separate  and  independent  mode  of  investiga- 
tion. We  should  rather  sav  that  observation,  in  the 
sense  in  which  we  have  used  the  word,  employs  experi- 
ment wherever  practicable  as  an  indispensable  auxiliary. 
The  methods  of  observation,  then,  which  have  still  to  be 
described,  will  in  many  cases  call  for  the  employment  of 
experiments.  Indeed,  it  will  be  seen  that  some  of  these 
are  essentially  methods  of  experimentation. 

§  49.  Explanation.  —  We  have  already  seen  that  the 
distinctiv)n  between  observation  and  explanation  is  not 
an  absolute  one.  The  task  which  thought  his  to  per- 
form —  the  task  which  is  undertaken  by  science  —  is  to 
reduce  the  isolated  and  chaotic  experiences  of  ordinary 
life  to  order  and  system.  And  it  is  important  to  remem- 
ber that  all  the  various  methods  employed  contribute 
directly  towards  that  result.  It  has,  however,  seemed 
possible  to  divide  this  undertaking  into  two  main  divis- 
ions. Observation,  it  was  said,  seeks  to  discover  the 
exact  nature  of  the  facts  to  be  dealt  with,  and  also  to 
determine  the  ways  in  which  they  are  necessarily  and 
invariably  connected.  But,  when  this  has  been  accom- 
plished, we  have  not  by  any  means  reached  an  end  of 
the  matter.  The  desire  for  knowledge  is  not  satisfied 
with  a  mere  statement  of  facts,  or  with  the  information 
that  certain  phenomena  always  occur  in  a  fixed  order 
as  antecedents  and  consequents.  Complete  knowledge 
demands  an  explanation  of  the  facts  as  thus  determined 


N   \i 


§  49-     KXPLANATION 


183 


by  the  methods  of  observation.  *  JF/r,'  we  ask,  'should  a 
always  precede  bV  '  W/iy  shouUl  dew  be  deposited  under 
such  and  such  conditions,  or  water  rise  thirty-two  feet  in 
a  pump  ? '  Science,  we  feel,  should  do  more  than  de- 
scribe the  facts ;  it  should  offer  an  explanation  of 
them  as  well.  To  explain  events,  however,  is  to  furnish 
reasons  for  them.  The  scientist  is  not  content  to  know 
merely  t/iat  such  and  such  phenomena  exist,  and  occur 
in  conjunction  with  each  other,  but  he  attenijits  to  dis- 
cover zv/iy  this  is  so.  His  knowledge  is  not  confined  to 
the  *  what,'  bui  mcludcs  the  *  why.'  It  is,  of  course,  true 
that  a  large  part  of  scientific  work  is  occupied  with  an 
attempt  to  determine  precisely  and  accurately  the  nature 
of  facts.  Until  the  facts  are  thus  scientifically  deter- 
mined attempts  at  explanation  are  usually  quite  futile. 
But  after  this  has  been  accomplished,  it  is  still  necessary 
to  show  reasons  why  the  phenomena  with  which  we  are 
dealing  have  the  precise  character  which  they  are  found 
to  possess,  and  why  they  should  occur  in  the  invari  ible 
order  in  which  they  are  observed.  Explanation,  in  other 
words,  completes  the  knowledge  obtained  through  ob- 
servation. It  does  further  intellectual  work  on  the 
results  given  by  the  latter  process.  Explanation,  itself, 
has  various  degrees  of  completeness  ;  it  may  be  more  or 
less  satisfactory.  When  we  come  to  treat  Analogy,  for 
example,  we  shall  find  that  it  affords  a  kind  of  expla- 
nation, though  not  one  of  an  entirely  satisfactory 
type.  In  general,  however,  we  may  say  that  explana- 
tion goes  bv./ond  the  particular  facts,  and  seizes  upon 
general  principles  or  laws  to  which  the  facts  are  re- 
ferred.    And  it  is  only  when  one  knows  the  general  law 


'  m 


I  'f- ' 


( 

1 

nanwfiMW  iL .,  jm» 


184 


THE    PROIJLEM    OF   INDUCTION 


or  principle  involved  in  the  case,  that  one  can  be  said 
really  to  understand  the  particular  facts. 

It  is  usually  said  that  where  we  know  merely  the  nature  of  phe- 
nomena, and  their  connection,  without  bein<;  able  to  explain  these 
facts,  our  knowlecl,t:je  is  empirical.  Tlius,  I  may  know  that  an  ex- 
plosion follows  tlie  contact  of  a  lighted  match  with  guni)owder,  or 
that  a  storm  follows  when  there  is  a  circle  around  the  moon,  without 
being  able  to  explain  in  any  way  why  these  facts  are  connected. 
On  the  other  hand,  if  we  can  connect  events  by  showing  the  gen- 
eral principle  involved,  we  say  that  our  knowledge  is  really  scientific. 
It  is  important  to  notice,  however,  that  empirical  knowledge  is  simply 
in  a  less  advanced  stage  than  the  scientific  knowledjie  which  has  sue- 
ceeded  in  gaii-lng  an  insight  into  the  general  law.  Empirical  know- 
ledge leaves  a  problem  which  intelligence  has  still  to  solve.  It  is,  of 
course,  true  that  a  large  part  of  everyone's  knowledge  is  empirical  in 
character.  We  all  know  many  things  which  we  cannot  explain.  In 
all  the  sciences,  too,  phenomena  are  met  with  which  seem  to  defy  all 
attempts  at  explanation.  Indeed,  some  of  the  sciences  can  scarcely 
be  said  to  have  '""assed  the  empirical  stage.  The  science  of  medi- 
cine, for  examp'.  .  hardly  yet  reached  any  knowledge  of  general 
principles.  Thp  ,  >.,.cir  v  knows,  that  is,  as  a  result  of  actual  ex- 
periment, that  such  ai.d  such  drugs  produce  such  and  such  effects. 
But  he  knows  almost  nothing  of  the  means  Vj  which  this  result  is 
achieved,  and  is  therefore  unable  to  go  beyond  the  fact  itself.  In 
this  respect,  he  is  very  little  better  off  than  the  ordinary  man,  who 
knows  that  if  he  eats  certain  kinds  of  food  he  will  be  ill,  or  if  he 
drinks  strong  liquors  in  excess  he  will  become  intoxicated. 


!li 


)C  said 


of  phe- 
lin  these 
t  an  cx- 
wder,  or 
,  without 
nnected. 
[he  gen- 
cientific. 
is  simply 
has  suc- 
al  l<now- 
It  is,  of 
pirical  in 
lain.    In 
)  defy  all 
scarcely 
of  medi- 
general 
ctual  ex- 
effects, 
result  is 
elf.     In 
lan,  who 
or  if  he 


CHAPTER   XIV 

METHODS   OF    OBSERVATION.  —  ENUMERATION    AND    STA- 
TISTICS 

§  50.  Enumeration  or  Simple  Counting.  —  We  shall 
begin  the  account  of  the  scientific  methods  with  Enu- 
meration. To  count  the  objects  which  we  observe, 
and  to  distinguish  and  number  their  parts,  is  one  of 
the  first  and  most  essential  operations  of  thought.  It  is 
of  course  true  that  qualitative  distinctions  precede  quan- 
titative. The  child  learns  to  distinguish  things  by  some 
qualitative  mark,  such  as  'black'  or  'hot,'  before  he  is 
able  to  count  them  (cf.  §  82).  But  we  '  ly  say,  never- 
theless, that  the  qualities  of  things  are  known,  m  a 
general  way  at  least,  before  scientific  procedure  begins. 
The  determination  of  quantity,  on  the  other  hand,  seems 
to  demand  a  more  conscious  effort  on  the  part  of  the 
mind.  We  learn,  that  is,  to  distinguish  the  general 
qualities  of  things  without  effort,  but,  in  order  to  obtain 
quantitative  knowledge,  it  is  necessary  to  set  ourselves 
deliberately  to  work.  We  may,  therefore,  take  Enumer- 
ation, or  Simple  Counting,  which  is  perhaps  the  easiest 
kind  of  quantitative  determination,  as  our  starting-point 
in  dealing  with  the  Inductive  Methods. 

A  considerable  step  in  advance,  in  the  task  of  re- 
ducing the  world  of  our  experience  to  order  and  unity, 
is  taken  when  we  begin  to  count,  ?'.('.,  to  group  together 

185 


^r 


186 


ENUMKRATIOX   AND   S  TV  IISTICS 


!  ■  W 


things  of  the  same  kind,  and  to  register  their  number. 
Thus  Tjiumeration  is,  to  some  extent,  also  a  process  of 
classification.  What  is  counted  is  always  a  collective 
whole,  the  units  of  which  are  either  all  of  the  same  kind, 
or  else  belong  to  a  limited  number  of  different  classes. 
Thus  one  might  determine  by  Enumeration  the  number 
of  sheep  in  a  flock,  taking  each  individual  as  belonging 
to  the  same  general  class,  '  sheep  ' ;  or  the  analysis  might 
be  pushed  further  so  as  to  give  as  a  result  the  number 
of  white  and  of  black  sheep  separately.  The  purpose 
for  which  the  enumeration  is  undertaken  always  deter- 
mines the  length  to  which  the  process  of  analysis  and 
distinction  is  carried.  For  example,  if  the  object  of  a 
census  enumeration  were  simply  to  determine  the  num- 
ber of  inhabitants  in  a  country,  it  would  not  be  neces- 
sary to  make  any  distinctions,  but  each  person  would 
'count  as  one.'  But  where,  as  is  often  the  case,  the 
aim  is  not  simply  to  count  the  sum-total,  but  also  to  de- 
termine the  relative  numbers  belonging  to  various 
classes,  analysis  has  to  be  pushed  further.  In  such 
cases,  we  might  count  the  number  belonging  to  each 
sex,  the  native-born,  and  those  of  foreign  birth,  those 
below,  and  those  above  any  given  age,  etc. 

It  will  be  noticed  that  the  process  of  enumeration 
takes  account  of  each  individual  instance.  And  the 
judgment  which  sums  up  the  process  puts  the  result  in 
a  numerical  form.  'There  are  twenty-five  thousand 
inhabitants  in  this  town,  five  thousand  of  whom  are  of 
foreign  birth.'  In  cases  where  the  examination  of  par- 
ticular instances  has  been  exhaustive,  the  result  may  be 
stated  in  the  form  of  a  universal  proposition.     Thus, 


§  50.     KNUMERAIIOX    OK   SIMTLK  COUXIIXC         1 8/ 


A\T 


I  : 


after  examining  the  calendar  of  each  of  the  months 
separately,  we  might  say  :  *  All  of  the  months  contain 
less  than  thirty-two  days.'  Or,  after  measuring  each 
individual  in  a  company,  the  assertion  might  be  made : 
'  No  one  in  this  company  is  more  than  six  feet  tall.' 
Cases  of  this  kind,  where  a  general  assertion  is  made 
after  an  examination  of  all  the  individuals  concerned, 
are  termed  by  Jevons,  instances  of  Pcj-fcxt  Indnction. 
"  An  Induction,  that  is  an  act  of  Inductive  reasoning,  is 
called  Perfect,  when  all  the  possible  cases  or  instances 
to  which  the  conclusion  can  refer,  have  been  examined 
and  enumerated  in  the  premises."  ^  On  the  other  hand, 
where,  as  usually  happens,  it  is  impossible  to  examine 
all  the  cases,  the  inductive  process  is  regarded  as  Im- 
perfect by  the  same  writer,  and  the  conclusion  expressed 
in  the  general  law  as  only  probable.  The  assertion 
that  all  the  months  of  the  year  contain  less  than  thirty- 
two  days,  is  derived  from  Perfect  Induction,  and  is  ab- 
solutely certain,  but  the  proposition  that  'all  men  are 
mortal,'  is  derived  from  Imperfect  Induction,  and  there 
is  no  certainty,  but  only  a  probability  that  all  future 
cases  will  agree  with  those  which  we  have  already 
experienced. 

This  distinction,  however,  seems  to  be  founded  on  a 
mistaken  view  of  the  nature  of  inductive  reasoning.  It 
assumes  that  it  is  the  business  of  induction  to  count 
instances.  When  the  examination  and  enumeration  is 
exhaustive,  the  results  can,  of  course,  be  summed  up  in 
a  general  proposition  which  is  absolutely  certain.     But 


(    f  1' 


w\ 


<i 


^  Jevons,  FUcmcntary  Lessons  in  Logic,  pp.  212-213. 


./,, 


■^^•CBW  l\  -..j.*9Mm 


i88 


ENUMERATION  AND  STATISITCS 


ii,i 


^ 


where  the  counting  is  incomplete,  where  all  the  possible 
cases  cannot  be  examined,  the  conclusion  is  regarded 
as  uncertain.  Now,  this  could  be  accepted  as  an  ac- 
count of  induction,  only  if  it  were  maintained  that  this 
process  aims  merely  at  a  summation  of  particular  in- 
stances. We  have  already  seen,  however,  that  the  real 
object  of  inductive  inference  is  to  discover  the  general 
law  or  principle  which  runs  through  and  connects  a 
number  of  particular  instances.  It  is,  of  course,  true 
that  we  shall  be  more  likely  to  obtain  a  correct  insight 
into  the  nature  of  the  law  from  an  examination  of  a 
large  number  of  cases  than  from  that  of  a  small  number. 
But  the  discovery  of  the  principle,  and  not  the  number 
of  instances,  is  the  main  point.  If  the  purpose  of  the 
induction,  the  discovery  of  the  universal  principle,  can 
be  adequately  attained,  one  case  is  as  good  as  a  hun- 
dred (cf.  §  88). 

The  tnith  seems  rather  to  be  that  enumeration  is  merely  the 
beginning,  rather  than  the  end  of  the  incUictive  process.  It  gives 
us  important  information  regarding  particular  instances  and  indi- 
viduals. But  in  itself  it  is  not  sufficient  to  bring  to  light  the  gen- 
eral law  that  explains  why  the  particular  objects  enumerated  are 
connected  together,  or  act  as  they  do.  Enumeration  plays  a  part 
as  a  method  of  observation,  but  it  affords  no  real  explanation  of 
the  particular  facts  with  which  it  deals.  Even  where  all  the  pos- 
sible cases  are  examined,  it  cannot  rightly  be  called  Perfect  In- 
duction, for  the  goal  of  Induction  is  explanation  by  means  of  a 
general  principle.  The  requirements  of  inductive  science  are  not 
completely  fulfilled,  for  example,  when  an  examination  of  Mercury, 
Venus,  Mars,  and  all  the  other  known  planets  yields  the  proposi- 
tion :  '  All  the  planets  revolve  around  the  sun  in  elliptical  orbits.' 
The  'alP  in  this  proposition  denotes  simply  an  aggregate  of  indi- 
viduals.    It  is  merely  an  expression  of  fact.     The  reasons  necessary 


\ 


§51.     STATISTICS   AND   Sl'A  TISTICAL   MEl'IIOUS       189 

to  explain  the  fiict  are  not  reached  by  enumeration  ;  in  order  to  ob- 
tain them  it  is  necessary  that  fiirtlier  worlc  shall  i)e  done  by  think- 
ing, and  that  the  process  of  induction  shall  be  carried  further. 

The  conclusion  which  we  reach,  then,  is  that  no 
process  of  enumeration  has  any  claim  to  the  title  of 
Perfect  Induction.  Enumeration  is  the  bep^innint;, 
rather  than  the  end  of  the  inductive  procedure. 
Nevertheless,  it  is  exceedingly  useful  as  a  preliminary 
step  and  preparation  for  scientific  explanation.  The 
number  of  stamens  and  pistils  which  a  plant  contains, 
or  the  number  of  tympanic  bones  possessed  by  an  ani- 
mal, is  often  of  the  g-rcatest  service  in  classification. 
And  classification,  although  it  is  by  no  means  the  end 
of  scientific  investigation,  is  in  many  of  the  sciences  a 
most  essential  and  important  step  towards  it.  The  task 
of  explaining  the  infinite  variety  of  natural  objects 
would  be  a  hopeless  one,  if  it  were  not  possible  to 
discover  similarities  of  structure,  in  virtue  of  which 
things  can  be  grouped  together  in  classes.  To  this, 
enumeration  in  a  very    .reat  degree  contributes. 


/ 


§  51.  Statistics  and  Statistical  Methods.  —  Statistical 
methods  depend  upon  enumeration.  They  aim  at  mak- 
ing the  process  of  counting  as  exact  and  precise  as  pos- 
sible. Modern  science  has  come  to  understand  that  its 
first  task  must  be  to  become  acquainted,  as  completely 
as  possible,  with  the  nature  of  the  facts  presented  to  it 
by  experience.  And,  for  this  purpose,  the  careful  classi- 
fication and  precise  enumeration  of  paiticulars  afforded 
by  statistics,  is  often  of  the  greatest  importance.  *'  The 
extent    to   which    the   statistical    method  prevails,  and 


:)||'^ 


,    .  :r|!J 


>MiHaniNMiili 


190 


EiNUMERATlOX   AND   STATISl'ICS 


:' 


I'! 


;i  J  ■! 


everything  is  counted,"  says  Professor  Sigvvart,  "is 
another  instance  of  the  fundamental  difference  between 
ancient  and  modern  science."  ^  It  would,  of  course,  be 
impossible  to  enter  here  into  a  full  description  of  the 
methods  employed  by  statistical  science.  The  method- 
ology of  every  science  must  be  learned  by  actual  prac- 
tice within  the  particular  field.  What  we  are  interested 
in  from  a  logical  point  of  view  is  the  purpose  which  sta- 
tistical investigation  seeks  to  fulfil,  and  the  part  which 
it  plays  in  rendering  our  knowledge  exact  and  syste- 
matic. 

We  notice,  in  the  first  place,  that  the  class  of  facts 
to  which  statistics  are  applied  has  two  main  character- 
istics :  the  subject  dealt  with  is  always  complex,  and 
capable  of  division  into  a  number  of  individual  parts  or 
units  ;  and,  secondly,  it  is  also  of  such  a  nature  that 
the  underlying  law  or  principle  of  the  phenomena  to  be 
investigated  cannot  be  directly  discovered.  Thus,  we 
employ  statistics  to  determine  the  death-rate  of  any 
country  or  community,  or  the  ratio  between  the  num- 
ber of  male  and  of  female  births.  It  is  clear  that  it  is 
impossible  to  make  use  of  experiment  when  we  are  deal- 
ing with  facts  of  this  kind,  because  the  conditions  are  not 
under  our  control.  If  it  were  possible,  for  example,  to 
determine  exhaustively  the  general  laws  according  to 
which  the  various  meteorological  changes  are  coordinated 
with  their  conditions,  we  should  not  trouble  ourselves  to 
count  and  register  the  separate  instances  of  changes  in 
the  weather.     Nor,  if  we  knew  exactly  the  general  condi- 

1  Logic  (Eng.  trans.),  Vol.  I.,  p.  286. 


§  5I-     SrAllSTICS   AND   STAriSllCAl-    MKIIIODS       I9I 


IS 


coiicli- 


» 


tions  uiulcr  which  any  given  human  organism  in  contact 
with  its  environment  would  cease  to  exist,  should  we 
count  the  individual  cases  of  death.  "  In  proportion  as 
we  are  unable  to  reduce  the  particular  event  to  rules  and 
laws,  the  numeration  of  particular  objects  becomes  the 
only  means  of  obtaining  comprehensive  propositions 
about  that  which  is,  for  our  knowledge,  fortuitous  ;  as 
soon  as  the  laws  are  found,  statistical  numeration  ceases 
to  be  of  interest.  There  was  some  interest  in  counting 
how  many  eclipses  f  the  moon  and  sun  took  place  year 
by  year,  so  long  as  they  occurred  unexpectedly  and  in- 
explicably ;  since  the  rule  has  been  foiuid  according  to 
which  they  occur,  and  can  be  calculated  for  centuries 
past  and  to  come,  that  interest  has  vanished.  But  we 
still  count  how  many  thunder-storms  and  hail-storms 
occur  at  a  given  place,  or  within  a  given  district,  how 
many  persons  die,  and  how  many  bushels  of  fruit  a 
given  area  produces,  because  we  are  not  in  a  position  to 
calculate  these  events  from  their  conditions."  ^ 

In  cases  like  those  mentioned  above,  where  we  are 
as  yet  unable  to  determine  the  general  laws  which  are 
at  work,  we  call  to  our  aid  statistical  enumeration. 
There  are  two  main  advantages  to  be  derived  from  the 
employment  of  this  method.  In  the  first  place,  it  con- 
tributes directly  towards  a  clear  and  comprehensive 
grasp  of  the  facts.  Instead  of  the  vague  impression  de- 
rived from  ordinary  observation,  statistics  enable  us  to 
state  definitely  the  proportion  of  fine  and  rainy  days 
during  the  year.     Statistical  enumeration    is  thus  one 

^  Sigwart,  Logic  (Eng.  trans.),  Vol.  II.,  p.  483. 


!^'4 


< 


■PBS^SSJWT— ^HW 


i 


192 


ENUMERATION   AND   STATISTICS 


|M         i' 


I!  !•; 


!1 


of  the  most  important  means  of  rendering;'  observation  ex- 
act and  trust wortliy,  and  of  summin^i;  up  its  results  in  a 
convenient  and  readily  intelligible  form.  It  is  of  the 
utmost  importance  when  dealin<;  with  complex  groups  of 
phenomena,  to  have  a  clear  and  comprehensive  view  of 
the  facts  of  the  case.  Thus,  when  trying  to  understand 
the  nature  of  society,  it  is  necessary  to  determine  accu- 
rately by  means  of  statistics,  such  facts  as  the  number 
of  male  and  of  female  births,  the  death-rate,  the  pro- 
portion of  marriages,  the  age  of  marriage,  etc.  But, 
m  the  second  place,  statistics  often  serve  to  reveal 
quantitative  correspondences  or  uniformities  between 
two  groups  of  phenomena,  and  thus  suggest  that  some 
causal  connection  exists  between  them.  It  is  found, 
for  example,  that  the  number  of  births  in  any  given 
country  varies  inversely  as  the  price  of  food  during  the 
previous  year.  Now  this  fact  at  once  suggests  the  ex- 
istence of  certain  physiological  and  psychological  laws 
which  may  serve  to  bring  these  facts  into  causal  rela- 
tion. In  many  cases,  such  correspondences  serve  only 
to  confirm  our  expectation  of  the  presence  of  a  causal 
law,  which  is  based  on  other  grounds.  Thus  we  should 
naturally  expect  that  there  would  be  a  relatively  greater 
number  of  cases  of  fever  in  a  town  which  had  an  insuf- 
ficient water  supply,  or  an  antiquated  system  of  sewer- 
age, than  in  a  town  where  these  matters  were  properly 
provided  for ;  and  statistics  might  bear  out  our  conclu- 
sions. In  general,  however,  it  may  be  said  that  causal 
laws  are  suggested,  not  by  corresponding  uniformities, 
but  by  corresponding  variations,  as  shown  by  the  sta- 
tistics of  different  sets  of  facts.     So  long  as  the  death- 


ion  ex- 
its in  a 
of  the 
[)ups  of 
'iew  of 
:rstantl 
e  ace  Il- 
ium her 
lie  pro- 
.     But, 
reveal 
etween 
t  some 
found, 
J  <;ivcn 
ine:  the 
the  ex- 
al  laws 
al  rela- 
e  only 
causal 
should 
>^Teater 
insuf- 
sevver- 
•operly 
conclu- 
causal 
•mities, 
le  sta- 
death- 


§51.    STATISTICS   AND   STAnsTICAl,   MKI'lIoDS       193 

rate,  for  example,  shows  a  constant  ratio  to  the  i)op- 
ulation,  no  causal  inference  is  sug<;este(l  ;  hut  if  the 
annual  nuniher  of  deaths  increases  or  decreases  consid- 
erahly,  we  are  led  to  look  for  some  variation  from  tlie 
normal  in  some  coincident  i;roup  of  phenomena.  And 
if  it  is  found  tliat  the  variation  in  the  death-rate  has 
heen  accompanied  l)y  unusually  favourable  or  unfavoura- 
ble conditions  of  weather,  the  presence  or  absence  of 
epidemics,  or  any  similar  circumstances,  there  will  be  at 
least  i\  pn'siimption  that  a  causal  relation  exists  between 
these  two  sets  of  events.  From  a  certain  likeness 
or  quantitative  resemblance  between  the  variations  of 
two  distinct  classes  of  phenomena,  we  are  led  to  the 
hypothesis  of  their  causal  connection. 

Statistical  enumeration  is  freciucntly  enii)loyed  to  determine  the 
avcrai^e  of  a  lai\<;e  number  of  instances  of  a  particular  kind.  This  is 
obtained  by  dividini;  the  sum  of  the  s^iven  numbers  by  the  number 
of  individuals  of  which  account  is  taken.  In  tliis  way  a  i^cneral 
averas;i'  is  reached  which  does  not  necessarily  correspond  exactly 
with  the  character  of  any  individual  of  the  group.  It  represents  a 
purely  imaijinary  conception,  which  omits  individual  ditTerences  and 
presents  in  an  abbreviated  form  the  general  character  of  a  whole 
cla.ss  or  group.  In  this  way,  by  the  determination  of  the  average,  it 
becomes  easier  to  compare  complex  groups  with  one  another.  Thus, 
if  the  average  height  of  Frenchmen  and  Englishmen  were  deter- 
mined, comparison  is  at  once  made  possible.  From  the  mean  or 
average  of  a  number  of  individuals,  or  set  of  instances,  however, 
we  can  infer  nothing  regarding  tlie  character  of  any  particular  indi- 
vidual, or  of  any  particular  instance.  What  /v  determined  by  the 
method  of  averages  is  the  general  nature  of  the  group,  as  represented 
by  the  average  or  typical  individual.  But  this  method  does  not  en- 
al)le  us  to  infer  anything  regarding  the  character  or  any  member  of 
the  group,  A,  or  B.      When  exact  statistics  are  obtainable,  however, 


I , 


V 


i 


! 


ii 


I '    « 


J!f 


]/ 


u- 


194 


KNUMKRAIION    AND   srAllSilCS 


it  is  possible  to  show  what  the  probalulttics  are  in  reference  to  any 
particular  case,  so  long  as  the  peculiar  circumstances  which  belong 
to  each  instance  are  not  considered,  and  each  case  is  reckoned  simply 
as  one  unit  of  the  group.  This  is,  of  course,  the  principle  employed 
by  the  method  of  m.ithematical  probabilities.  It  will  be  sufficient 
here  to  indicate  the  general  method  of  procedure  in  such  cases. 

§  52.  The  Calculation  of  Chances.  —  There  is,  of  course, 
no  such  thiuj;  as  *  chance,'  regarded  as  a  power  which 
controls  and  j^overns  events.  When  we  speak  of  some- 
things happening  'by  chance,'  or  of  some  occurrence  as 
*  probable,'  we  are  expressing  merely  a  deficiency  in  our 
own  knowledge.  "There  is  no  doubt  in  lightning  as 
to  the  point  it  shall  strike ;  in  the  greatest  storm  there 
is  nothing  capricious ;  not  a  grain  of  sand  lies  upon  the 
beach  but  infinite  knowledge  would  account  for  its  lying 
there  ;  and  the  course  of  every  falling  leaf  is  guided  by 
the  same  principles  of  mechanics  as  rule  the  motions  of 
the  heavenly  bodies."^  To  assert  that  anything  hap- 
pens by  chance,  then,  is  simply  to  confess  our  ignorance 
of  the  causes  which  are  operative. 

It  is  clear  that  we  are  in  this  position  regarding  many 
of  the  ordinary  events  which  belong  to  the  future.  Be- 
cause of  my  ignorance  of  the  causes  at  work,  I  can  only 
say,  *  It  may  rain  to-morrow.'  It  is  impossible  to  tell 
upon  which  side  a  penny  will  fall  at  any  particular 
throw,  or  what  card  may  be  drawn  from  a  pack.  But  in 
cases  like  these,  we  have  to  accept,  for  lack  of  anything 
better,  a  numerical  statement  of  the  chances  for  any 
particular   event.      Thus   we    know    that,    since   there 

1  Jevons,    The  Principles  of  Science^  Vol.  T.,  p.  225. 


I 


§.52.     IIIIC  CALCULATION   OF  CILVXCLS 


'95 


lire  only  two  sides  upon  which  a  penny  c:in  fall,  the 
chances  of  ihrowin*^  heads  in  any  trial  is  .\.  Similarly, 
there  are  four  chances  out  of  lifty-two  of  drawin^^  an 
ace  from  a  pack  of  cards.  The  chance  of  obtaininpj 
an  ace  by  any  draw  is  tlierefore  ^\,  =  ,l.j.  These  rij;urcs 
express  the  mathematical  chances.  Hxpericncc  of  a 
limited  number  of  instances  may,  however,  sometimes 
appear  to  show  a  lack  of  harmony  between  the  mathe- 
matical and  the  actual  chances.  Hut  in  proj)ortion  as 
the  number  of  trials  is  increased,  the  result  is  found  to 
a[)pro.\imate  more  and  more  nearly  to  the  mathematical 
expectation.  In  twenty  throws  of  a  penny  or  a  die,  we 
should  not  be  surprised  to  find  that  the  result  differed 
from  the  fraction  exi)rcssin<;  the  mathematical  chances. 
But  this  discrepancy  would  tend  to  disappear  as  the 
number  of  cases  was  increased.  Jevons  illustrated  this 
by  actual  trial,  using  a  number  of  coins  at  a  time.  Out 
of  a  total  of  20,480  throws,  he  obtained  a  result  of  10,353 
heads.  On  the  result  of  the  experiment  he  remarks  : 
"  The  coincidence  with  theory  is  pretty  close,  but  con- 
sidering the  large  number  of  throws  there  is  some 
reason  to  suspect  a  tendency  in  favor  of  heads."  ^ 

Apart  from  the  simple  and  somewhat  artificial  cases 
where  we  are  concerned  with  coins  and  dice,  etc.,  it  is 
impossible  to  determine  with  mathematical  precision  the 
chances  for  or  against  any  event.  In  cases  where  the 
whole  series  of  possibilities  does  not  lie  before  us,  we 
have  to  base  our  calculations  for  the  future  on  what 
is  known  regarding  the  frequency  with  which  the  events 


<«  m 


h  '^i 


V      » 


1  Jevons,  loc.  cit.  Vol.  L,  p.  230. 


mm 


^r 


% 


I  i 


Ff 


1,      ! 


1  '        il 


X\ 


Hi 


196 


ENUMERATION   AND   STATISTICS 


under  consideration  have  occurred  in  the  past.  Now 
the  results  of  the  last  paragraph  make  it  clear  that  it  is 
of  the  utmost  importance  that  the  statistics,  which  are 
taken  as  the  basis,  shall  be  as  full  and  comprehensive 
as  possible.  It  is  evident,  for  example,  that  serious 
errors  would  be  likely  to  arise,  if  the  death-rate  for  a 
single  year,  or  for  a  single  county  or  town,  were  taken 
as  typical  of  the  country  as  a  whole.  To  render  sta- 
tistics trustworthy,  they  must  be  extended  over  a  consid- 
erable period  of  time,  and  over  a  large  extent  of  country, 
so  as  to  eliminate  the  accidents  due  to  a  particular  time 
or  to  a  particular  locality. 

When  this  has  been  done,  however,  and  statistics  have  been  ob- 
tained that  have  a  right  to  be  regarded  as  really  typical,  the  chances 
in  any  individual  instance  can  be  readily  shown.  Thus  we  find  that 
out  of  one  thousand  children  born,  about  two  hundred  and  fifty  die 
before  the  age  of  six  years.  The  chances,  then,  at  birth,  that  any 
child  will  reach  this  age,  are  ^-^f^  or  \.  Again,  it  is  found  that 
only  about  two  persons  in  one  thousand  live  to  be  ninety  years  old. 
So  that  the  probability  of  any  child  living  to  this  age  would  be  ex- 
pressed by  the  fraction  j^%^  or  ■^\^.  This  is  essentially  the  princi- 
ple upon  which  life  insurance  companies  proceed.  Their  business  is 
conducted  on  tlie  assumption  that  there  will  be  an  approximately 
constant  death-rate,  though  they  cannot  foretell  what  particular  indi- 
viduals are  to  die  in  any  year.  It  thus  becomes  possible  to  calculate 
what  losses  from  death  may  be  expected  each  year.  Suppose  that 
it  is  found  that  the  annual  death-rate  among  men  of  a  certain  age 
throughout  the  country  is  twenty  out  of  every  thousand.  If  each 
man's  life  were  insured  for  $1000,  the  loss  to  the  company  from 
this  source  would  be  $20,000.  To  compensate  for  this  loss,  the 
company  would  be  obliged  to  demand  an  annual  payment  of  $20 
from  each  of  the  one  thousand  individuals  in  the  class.  Of  course, 
the  actual  computations  upon  which  insurance  is  based  in  concrete 


I 


I 


a 


•:i  Hi  i 


§  52.    THE   CALCUIATION   OF  CHANCES 


197 


Now 
hat  it  is 
lich  arc 
hensive 

serious 
:e  for  a 
e  taken 
der  sta- 

consid- 
:oimtry, 
iar  time 


been  ob- 

i  chances 

find  that 

fifty  die 
that  any 
und  that 
ears  old. 
d  be  ex- 
,e  princi- 
isiness  is 
ximately 
liar  indi- 
calculate 
lose  that 
tain  age 

If  each 
ny  from 
OSS.  the 
:  of  $20 

course, 
:oncrete 


cases  are  vastly  more  complex  than  this,  and  many  other  consider- 
ations arise  of  which  account  has  to  be  taken.  Rut  the  general 
principle  involved  is,  that  by  taking  a  sufficiently  large  number  of 
cases,  chance  can  be  almost  eliminated.  We  can  have  no  means 
of  determining  whether  any  healthy  individual  will  or  will  not  die 
before  the  end  of  the  year.  There  would  be  a  very  serious  risk, 
amounting  practically  to  gambling,  in  insuring  his  life  alone.  But 
the  transaction,  as  we  have  seen,  is  no  longer  a  mere  speculation 
when  a  large  number  of  individuals  are  concerned ;  for  the  actual 
loss  can  be  accurately  foretold  and  provided  for. 

References 

C.  Sigwart,  L^^^qt'c,  §§  loi,  102. 

J.  G.  Hibben,  Inductive  Logic,  Ch.  XV. 

L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Pt.  II.  Ch.  XI. 

J.  S.  Mill,  Logic,  Bk.  III.  Ch.  XVIII. 

B.  Bosanquet,  L(ygic,  Vol.  I.,  pp.  I28ff. 


%. 


'::>! 


W    • 


^'L 


V" 


'I 


i 


n 


! 


!i 


Ji'l 


.M 


r  .i 


CHAPTER   XV 

METHODS   OF    OBSERVATION 

Determination  of  Causal  Relation 

§  53.  Mill's  Experimental  Methods.  —  So  far,  we  have 
been  dealing  with  the  methods  employed  in  discovering 
the  nature  of  particular  things.  We  have  been  con- 
sidering how  our  knowledge  of  the  qualities  and  quanti- 
ties of  objects  may  be  made  as  exact  and  complete  as 
possible,  but  almost  nothing  has  yet  been  said  regard- 
ing the  connection  of  things.  Our  experience,  however, 
is  not  made  up  of  isolated  facts  and  events.  We  can 
scarcely  be  said  to  know  at  all,  until  we  become  aware 
that  certain  parts  of  our  experience  are  united,  like  the 
links  of  a  chain,  one  part  involving  another.  And,  as 
has  been  already  frequently  pointed  out,  the  growth  of 
knowledge  is  constantly  bringing  to  light  new  connec- 
tions between  facts  that  were  previously  taken  to  be 
independent  of  each  other.  Of  these  principles  of 
connection,  the  most  universal  and  important  is  that 
of  cause  and  effect.  Thus  we  say  that  everything 
^  which  happens  has  its  cause,  and  is  in  turn  followed 
by  its  effect.  What  rule,  or  rules,  can  now  be  given 
which  will  enable  one  to  discover  what  is  the  cause  or 
the  effect  of  an  event  in  any  particular  case  1 

Before  we  proceed  to  the  answer  of  this  question,  however,  it  is 
necessary  to  cxphiin  briefly  what  is  meant  in  science  by  the  relation 

198 


ii 


§  53-     MILL'S    i:xrERIMENTAL   METHODS 


199 


lil' 


t 


of  cause  and  effect.  As  the  terms  are  used  in  modern  scientific 
investigation,  a  cause  of  any  phenomenon  is  tliat  which  necessarily 
and  invariably  precedes  it ;  and  an  effect  is  what  follows,  in  the 
same  uniform  way,  some  event  which  has  gone  before  (cf  §  84). 
To  determine  the  causal  relation  between  phenomena,  then,  is  to 
discover  what  events  or  circumstances  always  accompany  each 
other  as  antecedent  and  consequent.  Now,  as  will  appear  when 
we  come  to  describe  the  methods  actually  employed,  it  is  very  often 
impossible  to  do  this  by  means  of  direct  observation.  Reasoning 
and  ex]jeriment  have  oftentimes  to  be  summoned  to  the  aid  of 
observation  in  distinguishing  between  events  wliich  are  merely 
accidentally  conjoined,  and  those  which  are  necessarily  connected 
as  cause  and  effects.  But,  as  has  been  already  .shown  (§§  48,  49), 
there  is  no  hard  and  fast  distinction  to  be  made  between  methods 
of  observation  and  methods  of  explanation.  To  discover  the  in- 
variable antecedent  of  a  phenomenon  is  at  least  the  beginning  of 
explanation.  Thus  B  is  explained  to  some  extent  when  I  am  able 
to  point  to  A  as  its  lavariable  antecedent.  Nevertheless,  since  this 
connection  of  A  and  B  is  itself  a  fact  which  may  be  observed,  its 
discovery  may,  I  think,  be  fairly  said  to  belong  to  observation  rather 
than  to  explanation.  Explanation,  in  its  complete  form,  carries  one 
beyond  the  mere  fact  of  connection  to  its  reasons.  At  the  stage 
we  have  now  reached,  however,  the  problem  is  to  show  what  other 
phenomenon,  or  group  of  phenomena,  is  necessarily  and  uniformly 
connected  with  a  given  event  or  circumstance. 


I' I 

M 

•.ll 


'  »  "  I 


^■f 


The  methods  by  which  such  a  law  of  connection  may 
be  established  were  first  formulated  by  Mill  in  his  Logic. 
He  stated,  in  general  terms,  the  principles  which  were 
already  in  use  in  scientific  procedure.  Mill  gives  five 
separate  canons,  but,  as  he  himself  recognizes,  there 
are  but  two  main  principles  involved.  "  The  simplest 
and  most  obvious  modes  of  singling  out  from  among 
the  circumstances  which  precede  or  follow  a  phenome- 
non, those  with  which    it    is   really  connected   by   an 


:     t        1, 

.1 

«' 

1 

mmmam 


^isaa 


m6 


n 


i  1 


200 


CAUSAL   DETERMINATION 


invariable  law  are  two  in  number :  One  is  by  com- 
paring together  different  instances  in  which  the  phe- 
nomenon occurs.  The  other  is  by  comparing  together 
instances  in  which  the  phenomenon  does  occur  with 
instances  in  othci'  respects  similar  in  which  it  does  not. 
These  two  methods  may  be  respectively  denominated 
the  Method  of  Agreement,  and  the  Method  of  Differ- 
ence." ^  Of  the  other  three  methods  mentioned  by 
Mill,  one  —  the  Joint  Method  of  Agreement  and  Dif- 
ference —  is,  as  the  name  implies,  a  direct  combination 
of  the  first  two,  while  the  Method  of  Residues  and  the 
Method  of  Concomitant  Variations  are  corollaries  from 
the  same  principles.  We  shall  now  proceed  to  state 
and  illustrate  these  canons. 

§  54.  The  Method  of  Agreement.  —  The  principle  upon 
which  this  method  proceeds  is  stated  in  the  following 
way  by  Mill :  *'//  tzvo  or  more  instances  of  the  pJicnome- 
non  under  investigation  have  only  one  circumstance  in 
common^  the  circumstances  in  ivhich  alone  all  the  in- 
stances agree  is  the  cause  {or  effect)  of  the  given  phenome- 
non.'' The  purpose  of  this  rule,  it  will  be  remembered, 
is  to  help  us  to  determine  what  particular  facts  in  our 
experience  are  connected  as  causes  and  effects.  If  the 
problem  is  to  find  the  cause  of  some  phenomenon,  the 
canon  may  be  illustrated  in  the  following  way.  Let 
P^,  P2,  P^  represent  different  instances  of  a  phenome- 
non, P,  whose  cause  is  to  be  ascertained.  And  suppose 
that  we  are  able  to  analyze, 

1  Mill,  F.ogii-,  r.k.  III.  Ch.  VIII.  §  1 


§  54-    THE   METHOD   OF  AC'.REEMENT 


20I 


the  antecedents  of  P'  into  abed ; 
the  antecedents  of  P^  into  i^fcm ; 
the  antecedents  of  P^  into  klnc. 

Now  it  is  clear  that  c  is  the  sole  circumstance  in  which 
the  antecedents  of  all  these  instances  of  P  agree.  We 
should  be  justified  in  concluding,  therefore,  according  to 
this  method,  that  c  is  probably  the  cause  of  the  phe- 
nomenon under  investigation,  P.  We  may,  then,  adopt 
Jevons's  formula  for  discovering  the  cause  of  any  given 
phenomenon  by  this  method  :  ''TJic  sole  invariable  ante- 
cedent of  a  phenomenon  is  probably  its  eanse." 

If,  now,  we  wished  to  discover  the  effect  of  some- 
thing which  happens,  it  would  be  necessary  to  deter- 
mine, by  observing  a  number  of  instances,  what  common 
circumstance  can  be  found  among  the  events  which 
follow  it. 

If  Q^  were  followed  hy  /jf/d\ 

and  Q-  were  followed  by  lni^<^e, 

and  Q'^  were  followed  by  ^rst, 

we  should  be  able  to  say  that  O  and  i^  were  connected 
as  cause  and  effect.  The  rule  might  then  be  expressed  : 
T/ie  sole  invariable  consequent  of  a  phenomenon  is  prob- 
ably its  effect. 

When  antecedents  and  consequents  are  thus  repre- 
sented schematically  by  means  of  letters,  it  is  easy  to 
perceive  at  once  the  common  circumstance  in  a  number 
of  instances.  But  the  facts  and  events  of  the  real  world 
are  not  separated  off  from  each  other  in  this  way.  The 
common  circumstance  in  which  a  number  of  instances 
agree  has  to  be  separated  out  by  analysis  from  the  varia- 


.  »t 


gi!-    i' 


III 


202 


CAUSAL    DETERMINATION 


I 


mm 


H   i 


ble  elements  which  form  part  of  the  different  antecedents 
and  consequents.  In  order  to  discover  the  common 
characteristic,  it  is  necessary  that  we  should  be  able 
to  analyze  a  complex  phenomenon  into  its  constituent 
parts,  and  should  also  be  able  to  recognize  it  as  com- 
mon, though  it  may  appear  in  wholly  different  circum- 
stances. This  will  become  evident  by  considering  a 
number  of  concrete  cases  in  which  this  method  may 
be  employed. 

If  a  number  of  cases  of  typhoid  fever  were  to  appear 
at  about  the  same  time  in  a  community,  one  would  nat- 
urally wish  to  explain  this  phenomenon  by  tracing  it  to 
its  cause ;  and  to  do  this  one  would  try  to  discover 
some  circumstance  which  was  the  common  antecedent 
of  all  the  cases.  The  water  supply  might  first  be  ex- 
amined. But  if  it  were  found  that  this  were  derived 
from  entirely  different  sources  in  the  different  cases,  we 
should  probably  conclude  that  the  explanation  must  be 
sought  elsewhere.  Suppose  that  as  a  result  of  careful 
analysis  it  was  discovered  that  all  the  individuals  pros- 
trated with  the  fever  had  eaten  oysters  bought  at  the 
same  market.  If  this  were  the  only  common  circum- 
stance discoverable  after  careful  investigation,  we  should 
conclude  that  probably  the  oysters  were  the  cause  of 
the  fever.  The  process  of  analysis  could  be  pushed 
still  further,  if  one  wished,  in  order  to  determine  more 
exactly  the  precise  source  of  the  infection  ;  e.£:,  it  might 
be  found,  as  a  result  of  further  inquiry,  that  the  water 
in  which  the  oysters  were  kept  was  vitiated  by  a  sewer. 

Another  example  of  the  method  of  agreement  which 
is  often  quoted  by  logicians  may  be  given.     Ore  would 


§  54-     THE   METHOD  OF  AGREEMExNT 


203 


\ 


naturally  suppose  that  the  colours  and  line  of  mother-of- 
pearl  were  due  to  the  chemical  or  physical  character  of 
the  substance  itself.  Sir  David  Brewster,  however, 
liappened  to  take  an  impression  of  a  piece  of  mother- 
of-pearl  in  beeswax  and  resin,  and  was  surprised  to  see 
the  colours  reproduced  upon  its  surface.  He  then  took 
a  number  of  other  impressions  in  balsam,  gum-arabic, 
lead,  etc.,  and  found  the  iridescent  colours  repeated  in 
every  case.  In  this  way  he  proved  that  the  colours  were 
caused  by  the  form  of  the  substance,  and  not  by  its 
chemical  qualities  or  physical  composition.  The  dif- 
ferent substances,  wax,  balsam,  lead,  etc.,  in  which  the 
phenomenon  of  colour  appeared,  had  nothing  in  common 
except  the  form.  This,  therefore,  according  to  the 
method  of  agreement,  was  properly  regarded  as  the 
cause  of  the  phenomenon  to  be  explained. 

An  example  of  the  application  of  this  method  to  the 
discovery  of  the  effect  of  a  phenomenon  may  now  be 
given.  Let  us  suppose  that  the  problem  is  to  determine 
the  effect  of  some  proposed  legislation.  It  is  necessary, 
of  course,  to  refer  to  other  instances  where  this  legisla- 
tion has  been  put  in  force.  Let  us  suppose  that  in  one 
case  what  followed  the  enactment  of  the  law  under  con- 
sideration was  falling  off  of  revenue,  increase  of  immi- 
gration, good  crops,  etc.,  and  in  a  second,  revival  of 
ship-building,  rainy  weather,  and  increase  of  immigra- 
tion ;  and  that  in  other  instances  where  still  other 
conditions  prevailed,  the  number  of  immigrants  still 
continued  to  increase.  Since  this  latter  circumstance  is 
the  only  one  which  follows  invariably  upon  the  enact- 
ment of  the  law,  we  are  justified  in  concluding,  after  a 


i 


I.  < 


:'H. 


inil 


,      .|ji.;r 


pf^m^^mfrwi^gwrn 


"r 


■. 


II 


'il' 


11 


{%■ 


1 

1          : 

Ti'S 

Jh 

:      . 

^' 

fl  - 

k\     u 

4 

t  i 

li  ., 

204 


CAUSAL    DI/IERMINATION 


certain  iniml)cr  of  ()l).scrvations,  that  it  is  necessarily 
connected  with  tlie  law  as  its  result.  It  is  important 
to  note  that  the  conclusions  reached  by  this  method 
are  greatly  strengthened  by  increasing  the  number  of 
observations,  and  by  taking  instances  as  dissimilar  in 
character  as  possible. 

The  method  of  A<:^reement  by  itself,  however,  is  not  al)le  to 
/  afford  us  certainty  in  every  case.  We  have  spoken  of  the  cause  as 
n/  'tlie  invarialjle  antecedent,'  and  of  the  effect  as  '  the  invarial)le  con- 
sequent.' So  long,  then,  as  wc  are  dealing  with  events  which  fol- 
low each  other,  there  is  no  difficulty  in  perceiving  which  is  cause, 
and  which  effect.  But  we  au  often  called  upon  to  investigate  the 
relation  between  phenomena  that  are  more  permanent  in  character. 
And  it  is  tlicn  not  at  all  easy  to  determine  by  means  of  the  method 
of  Agreement  which  is  cause  and  which  is  effect.  Poverty  and  in- 
temperance, for  example,  are  found  conjoined  so  frequently  as  to 
make  it  evident,  apart  from  other  considerations,  that  some  causal 
relation  exists  between  them.  It  might  be  maintained  with  appar- 
ently equal  show  of  reason,  that  the  former  is  the  cause,  or  the  effect, 
of  the  latter.  Again,  is  one  to  say  that  ignorance  is  the  cause  or  the 
effect  of  moral  degradation?  There  seems  to  be  no  method  of  de- 
termining which  is  antecedent  and  which  consequent.  As  a  matter 
of  fact,  it  is  probably  true  in  such  cases  that  the  phenomena  act 
and  react  upon  each  other :  that  each  term,  in  other  words,  is  at 
once  both  cause  and  effect. 

There  is  still  another  circumstance  which  renders  uncertain  the 
results  of  the  method  of  Agreement.  We  have  pioceeded  on  the 
assumption  that  the  given  phenomenon  is  always  produced  by 
the  same  cause ;  and,  on  the  other  hand,  that  the  effects  of  different 
caures  are  always  different.  lUit  this  is  not  so ;  heat,  for  example, 
may  be  caused  by  combustion,  or  by  friction,  or  electricity.  This 
is  what  is  meant  by  the  phrase  '  Plurality  of  Causes.'  Again, 
neither  the  cause  nor  the  effect  need  be  composed  of  a  simple  phe- 
nomenon, or  single  circumstance,  as  has  been  supposed.     Indeed,  so 


§55-    'I'l'K    Mirniol)  OK   DIFl-KkKXCH 


205 


sssarily 
portant 
method 
iber  of 
lilar  in 


able  to 
cause  as 
ble  C(in- 
liich  foi- 
ls cause, 
i,u;ate  the 
haracter. 
:  method 
^  and  in- 
ly as  to 
le  causa! 
h  appar- 
le  effect, 
se  or  the 
d  of  de- 
a  matter 
iiena  act 
ds,  is  at 

tain  the 
on  the 
iced  by 
different 
example, 
'.  This 
Again, 
)le  phe- 
deed, so 


far  as  observation  can  show,  antecedent-,  and  consequents  usually 
seem  to  consist  of  complex  sets  of  circumstances.  The  diflicully 
with  the  method  of  Agreement  is  that  it  does  not  push  the  process 
of  analysis  far  enough  to  enable  us  to  establish  comptetely  a  law  of 
causal  relation.  The  fact  of  Agreement  between  phenomena  often 
serves,  however,  to  sir^X'^''''^  '^  I'l^^'  of  connection.  This  law  has  after- 
wards to  be  tested  by  the  other  methods,  especially  by  the  method  of 
Difference. 

§  55.  The  Method  of  Difference.  —  Accordingly  to  the 
method  of  Agreement,  we  compare  a  nimiber  of  diverse 
instances,  in  all  of  which  a  given  phenomenon  occurs, 
and  endeavour  to  discover  some  circumstance  which 
is  invariably  present.  The  method  of  Difference,  on 
the  other  hand,  compares  an  instance  in  whicli  a  phe- 
nomenon occurs  with  another  as  nearly  similar  to  it 
as  possible,  in  which  it  does  not  occur.  Its  canon  is 
expressed  by  Mill  as  follows  :  ''  If  a)i  instance  in  which 
the  phenomenon  under  investigation  occurs,  and  an  in- 
stance in  ivhich  it  does  not  occur,  have  every  circum- 
stance in  common  save  one,  that  one  occurring  only  in 
the  former ;  the  circumstance  in  ivhich  alone  the  tzvo 
instances  differ  is  the  effect  or  the  cause  or  an  indis- 
pensable part  of  the  cause,  of  the  phenomenon^  It 
will  perhaps  make  the  matter  clearer  to  say :  *  whatever 
is  present  in  a  case  when  the  phenomenon  to  be  inves- 
tigated occurs,  and  absent  in  another,  when  that  phe- 
nomenon does  not  occur,  other  circumstances  remaining 
the  same,  is  causally  connected  with  that  phenomenon.' 
That  is,  by  means  of  this  method  we  compare  two 
instances  which  differ  only  in  the  fact  that  the  phe- 
nomenon in  which  we  are  interested,  is  present  in  the 


I. 


\ 


I 


\  '■' 


i 

» 

1     (■  . 

206 


CAUSAL   DETl^RM [NATION 


',«,; 


m  tfi 


I       i        .;' 


it;  i   ! 


one,  and  absent  in  the  other, 
represented  in  this  way, 


If  now  the  two  cases  are 


PHK  conjoined  with  a/^, 
and    Ills,  conjoined  with   /^, 

we  conclude  at  once  that  P  is  causally  connected  with  a. 

Almost  any  instance  in  which  experiment  is  cm- 
ployed  will  serve  to  illustrate  this  methotl.  If  a  bell  is 
rung  in  a  jar  containing  air,  the  sound  will  of  course  be 
heard  at  any  ordinary  distance.  But  after  having  re- 
moved the  air  by  means  of  an  air-pump,  let  the  bell  be 
again  struck.  It  will  now  be  found  that  the  sound  is  no 
longer  heard.  When  the  two  cases  are  compared,  it  is 
at  once  evident  that  the  only  difference  in  the  antece- 
dents is  the  presence  of  the  air  in  the  one  case,  and  its 
absence  in  the  other.  When  the  air  was  prepent,  the 
sound  was  heard  ;  when  it  was  absent,  the  sound  was 
not  heard.  We  conclude,  therefore,  that  the  perception 
of  30und  is  causally  connected  with  the  presence  of 
atmospheric  air.  Again,  we  can  prove  that  the  so-called 
'taste  '  of  different  objects  depends  upon  smell,  by  tast- 
ing, say,  an  orange,  and  after  a  little  time  has  elapsed, 
tastins:  it  a  second  time  while  holding  the  nose.  It 
will  be  found  in  this  latter  case  that  instead  of  the 
familiar  'orange  taste,'  one  senses  merely  'acid,'  or 
'sweet.'  The  only  difference  in  the  two  trials  being 
that  in  the  former  the  organ  of  smell,  which  was  ex- 
cluded in  the  latter,  was  operative,  the  so-called  'orange 
taste '  is  proved  to  be  due  to  smell  rather  than  to  taste 
proper. 

An  essential  requirement  of  the  method  of  Difference 


§55-    'll'l-:    MKTIIOD   OF   DIFFFRKNCl-: 


207 


being 


i 


is  that  a/i/j'  one  cinnmstaua  sJiall  he  varied .j2M--iL.Ji}nc._ 
The  object  of  the  nietliod  is  to  isolate  the  various  con- 
ditions which  go  to  make  u{)  a  complex  phenomenon, 
in  order  that  we  may  mark  the  effect  of  the  presence 
or  absence  of  each  one  individually.  Now,  in  observing 
what  goes  on  in  nature,  we  rarely  find  changes  in 
which  but  a  single  element  has  varied.  If  we  find  that 
to-day  is  cooler  than  yesterday,  we  may  be  inclined  to 
refer  the  change  to  the  thunder-storm  of  last  night. 
But  rain  also  accompanied  the  thunder-storm,  and  the 
direction  of  the  wind  has  changed.  So  that  it  is  im- 
possible in  such  cases  to  apply  the  method  of  difference. 
To  employ  this  method  successfully,  observation  must 
usually  be  sui)plemented  by  experiment.  In  performing 
experiments,  we  determine  what  conditions  are  to  be 
operative,  and  arrange  the  apparatus  so  as  to  carry  out 
our  purpose.  Having  thus  control  of  the  conditions,  we 
are  able  to  vary  them  at  pleasure.  In  this  way,  experi- 
ment becomes  an  instrument  by  means  of  which  analysis 
can  be  carried  further  than  is  possible  for  unaided  ob- 
servation. It  enables  us  to  separate  things  which  are 
usually  conjoined,  and  to  observe  the  result  of  each  when 
taken  by  itself.  In  employing  experiment,  however,  the 
greatest  care  must  always  be  taken  to  introduce  only 
one  new  condition  at  a  time,  or  at  least  only  one  new 
circumstance  which  can  in  any  way  influence  the  result. 
It  often  happens,  too,  as  Jevons  points  out,  that  the 
experimenter  is  not  aware  of  all  the  conditions  which 
arc  operative  when  his  investigations  arc  made.  "  Some 
substance  may  be  present,  or  some  power  may  be  in 
action   which   escapes   the   most   vigilant    examination. 


t/ 


«.  I> 


HA 


h\'>. 


fr 


CAUSAI,   UintRMlXAilON 

Not  bciiij,^  aware  of  its  existence,  we  arc  of  course 
unable  to  take  proper  measures  to  exclude  it,  and  thus 
determine  the  share  which  it  may  have  in  the  results  of 
our  experiments."  ^  For  this  reason,  it  is  always  neces- 
sary that  experiments  should  he  repeated  by  different 
persons  ami  so  far  as  possible  under  varying  conditions. 
I  c|uote  two  examples  from  the  work  of  Jevons  to  which 
reference  has  just  been  made. 

"One  of  the  most  cxtiaordiiKiry  instances  of  an  erroneous  opinion 
due  to  overlookins^  intcrferint;  a;j;cnts  is  that  concerning  the  increase 
of  rainfall  near  the  earth's  surface.  More  than  a  century  a<i;o  it  was 
observed  that  rain  <i;auf;es  placed  upon  church  steeples,  house-to[)s, 
and  other  elevated  places,  gave  considerably  less  rain  than  if  they 
were  on  the  i^round,  and  it  has  very  recently  been  shown  that  the 
variation  is  most  rapid  in  the  close  nei.nhborhood  of  the  j^round. 
All  kinds  of  theories  have  ])een  started  to  explain  this  phenomenon  ; 
but  I  have  attempted  to  show  that  it  is  simply  due  to  the  interfer- 
ence of  wind  which  deflects  more  or  less  rain  from  all  the  gauges 
which  are  at  all  exposed  to  it. 

"  The  great  magnetic  power  of  iron  renders  it  a  constant  source  of 
disturliance  in  all  magnetic  experiments.  In  building  a  magnetic 
observatory  great  care  must  be  taken  that  no  iron  is  employed  in 
the  construction,  and  that  no  masses  of  iron  are  near  at  hand.  In 
some  cases,  magnetic  observations  h  been  seriously  disturbed  l)y 
the  existence  of  masses  of  iron  in  the  neighborhood.  In  Faraday's 
experiments  upon  feebly  magnetic  or  diamagnetic  substances,  he 
took  the  greatest  precautions  against  the  presence  of  any  disturbing 
substance  in  the  copper  wire,  wax,  paper,  and  other  articles  used  in 
suspending  the  test  objects.  It  was  his  invariable  custom  to  try  the 
effect  of  the  magnet  upon  the  apparatus  in  the  absence  of  the  object 
of  experiment,  and  without  tliis  preliminary  trial  no  confidence 
could  be  placed  in  the  results."  - 

1  Jevons,  Pyiuciplcs  of  Science  ^  Vol.  IT.  p.  37. 
-  Jevons,  op.  cit.  pp.  40,  41. 


I 


course 
id  thus 
suits  of 
i  ncccs- 
iffcrcnt 
ditious. 
0  which 


IS  opinion 
;  increase 
Lj^o  it  was 
3Use-tops, 
vn  if  tliey 
i  that  the 
e  ground, 
nonienon ; 
i  interfer- 
he  gauges 


source 


of 


magnetic 
ployed  in 
md.  In 
turbed  by 
'araday's 
V  he 
isturbing 
used  in 
to  try  the 
he  object 
onfidence 


}S 


CIIAITKR    XVI 

METHODS    OF    OIJSEKVATION 

Dctcnninatioii  of  Causal  Relation  {conti fined) 

§  56.    The  Joint  Method  of  Agreement  and  Difference.  — 

When  it  is  not  [iossiblc  to  ()l)tain  cxi)erinieiitaj  proof 
directly,  recourse  is  often  had  to  what  Mill  has  called 
the  joint  method  of  Agreement  and  Difference.  This 
writer  has  given  the  following  expression  of  the  canon  : 
"  If  two  or  more  instances  in  which  the  /phenomenon 
occurs  have  only  one  circnmstance  in  common,  ivJiile 
tivo  or  more  instatices  in  wJiich  it  does  not  occur  have 
nothing  in  common  save  the  absence  of  that  circnm- 
stance, the  circumstance  in  zvhich  alone  the  two  sets 
of  instafices  differ  is  the  effect,  or  the  cause,  or  an 
imlispensahle  part  of  the  cause,  of  the  phenomenofi.'* 
This  method,  as  the  name  implies,  is  a  combination 
of  the  two  already  described.  We  may  perhaps  sim- 
plify Mill's  canon  somewhat  by  putting  the  matter  in 
the  following  way :  A  number  of  instances  havifig  I 
been  examined,  zvhatever  is  invariably  pi f sent  when 
the  phenomenon  under  investigation  is  present,  and 
invariably  absent  ivJien  the  latter  is  absent,  is  causally  ' 
connected  with  that  phenomenon.  By  the  help  of  this 
method,  the  weakness  which  has  already  been  noticed 
in  the  method  of  Agreement  is  overcome.  We  first 
F  209 


'it'l« 


'■■ii 


r'hi 


u    ,  i 


K  > 


^•»^-w"'    •J-'«"^kpA. 


V 


i 


Dmm 


t  \ 


'iim 


I  '.*■ 


14 


2IO 


CAUSAL   DETERMlNAllOxN 


compare  different  instances  in  whicli  the  phenomenon 
occurs,  if  these  arc  found  to  agree  in  only  a  single 
circumstance,  we  conclude,  according  to  the  canon 
of  Agreement,  that  this  circumstance  is  probably  con- 
nected causally  with  the  phenomenon  in  which  we  are 
interested.  But  the  proof  is  not  yet  complete.  To 
really  prove  the  connection,  we  must  show  that  where- 
ever  this  circumstance  is  absent,  there  the  phenome- 
non is  also  absent. 

As  an  illustration  of  this  method,  we  may  take  the 
case  where  one  is  trying  to  decide  whether  some  stimu- 
lant like  coffee  or  tobacco  is  injurious  to  him  or  not.  If  a 
person  found  himself  troubled  with  insomnia  or  nervous- 
ness while  in  the  habit  of  smoking,  he  might  suspect"  that 
this  was  the  cause.  That  is,  the  coincidence  or  Agree- 
ment between  the  habit,  and  ill-health  would  suggest  a 
causal  relation.  But  as  yet,  the  relation  would  be  only 
suggested,  not  proved.  The  method  of  Agreement,  as 
we  have  already  seen,  only  gives  us  probable  conclu- 
sions. Here,  however,  we  have  the  conditions  under 
our  control,  and  can  resort  to  experiment  and  the 
method  of  Difference,  in  order  to  verify  or  disprove  the 
suggestion.  If  after  having  given  up  smoking  for  a 
reasonable  length  of  time,  a  man  found  that  the  dis- 
agreeable symptoms  still  continued,  he  would  conclude 
that  his  suspicion  v/as  unfounded.  But  if  it  were  found 
that  his  insomnia  and  nervousness  had  disappeared 
during  his  period  of  abstinence,  and  if  no  other  circum- 
stance in  his  mode  of  life  had  been  varied  in  the  mean- 
time, he  would  be  forced  to  admit,  however  reluctant  he 
might  be  to  do  so,  that  the  troublesome  physiological 


! 


lomenon 
a  single 
e  canon 
ibly  con- 
h  we  are 
:;te.  To 
It  wherc- 
)henome- 

take  the 
le  stimu- 
lot.     If  a 
nervoiis- 
pect  that 
tr  Agree- 
uggest  a 
be  only 
ment,  as 
I  concl Il- 
ls under 
and     the 
rove  the 
o-  for   a 
the  dis- 
con  elude 
re  found 
ippeared 
circum- 
e  mean- 
ctant  he 
iological 


§57.     THE   METHOD    OE   CONCOMITANI'    VARIATIONS     211 

derangements  were  probably  connected  with  the  smok- 
ing habit. 

§  57.   The   Method  of   Concomitant  Variations.  —  The 

methods  of  Agreement  antl  Difference  are  employed, 
as  we  have  seen,  to  determine  what  events  are  necessa-\x' 
rily  connected  as  causes  and  effects.  By  examining  a 
considerable  number  of  instances,  and  by  comparing 
the  cases  in  which  the  phenomenon  of  interest  to  us 
occurs,  with  cases  in  which  it  docs  not  occur,  we  seek 
to  rule  out  all  accidental  and  unessential  conjunctions. 
But  as  yet  nothing  has  been  said  of  qitimtitatvoe  rela- 
tions. The  discovery  of  a  quantitative  agreement  or  cor- 
respondence between  two  phenomena,  or  two  groups  of 
phenomena,  often  enables  us  to  discover  a  causal  relation 
between  them(cf.  pp.  192-193).  Moreover,  science  does 
not  rest  satisfied  with  the  mere  discovery  and  description 
of  changes,  and  the  order  in  which  they  occur.  We  may 
almost  say  that  science  does  not  exist  until  the  quanti- 
tative aspects  of  phenomena  are  taken  into  account  — 
until  things  are  weighed  and  measured.  The  physicist 
does  not  think  his  work  finished  when  he  has  discovered 
that  sound  is  produced  by  atmospheric  vibrations.  He 
carries  on  his  analysis  until  he  can  discover  the  quanti- 
tative relations  between  the  amplitude  and  velocity  of 
the  vibrations,  and  the  loudness  and  pitch  of  the  result- 
ing tone.  And  the  psychologist  is  not  satisfied  with  the 
general  statement  that  certain  sensations  are  causally 
connected  with  certain  kinds  of  stimulus  ;  but  he  seeks 
to  discover,  whenever  possible,  the  exact  quantitative 
relation  between  sensation  and  stimulus.     In  short,  the 


'  ^l<)l<i<fc»^ 


212 


CAUSAL   DETERMINATION 


J 


most  important  ieaturc,  the  very  essence,  one  may  say, 
of  modern  scientific  investigation,  is  the  establishment 
of  quantitative  relations. 

Looking  at  two  things  from  the  standpoint  of  quan- 
tity, then,  we  say  that  when  their  variations  keep  pace 
with  each  other,  they  are  in  some  way  causally  con- 
nected.. The  following  is  Mill's  statement  of  the  canon  : 
^'  WJiatcvcr  phenomenon  varies  in  any  manner  ivhenever 
another  phenomenon  varies  in  a  partieular  manner,  is 
cither  a  cause  or  an  effect  of  that  pJienomenon,  or  is  con- 
nected with  it  througJi  some  fact  of  causation!'  The 
illustrations  of  this  law  given  by  Jevons  are  so  excellent 
that  we  cannot  Ju  better  than  adopt  them  :  — 

"  The  illustrations  of  tills  law  are  infinitely  numerous.  Thus 
l\Tr.  Joule,  of  Manchester,  conclusively  proved  that  friction  is  a  cause 
of  heat  by  expending  exact  quantities  of  force  by  rubbing  one  sub- 
stance against  another,  and  showed  that  the  heat  produced  was 
exactly  greater  or  less  in  proportion  as  the  force  was  greater  or  less. 
We  can  apply  the  method  to  many  cases  which  had  previously  been 
treated  by  the  simple  method  of  difference  ;  thus  instead  of  striking 
a  bell  in  a  complete  vacuum,  we  can  strike  it  with  a  very  little  air  in 
the  receiver  of  the  air-pump,  and  we  then  hear  a  very  faint  sound 
wliich  increases  or  decreases  every  time  we  increase  or  diminish  the 
density  of  the  air.  This  experiment  conclusively  satisfies  any  per- 
son that  air  is  the  cause  of  the  transmission  of  sound. 

'•  It  is  this  method  which  often  enables  us  to  detect  the  material 
connection  which  exists  between  two  bodies.  For  a  long  time  it 
had  been  doubtful  whether  the  red  flames  seen  in  total  eclipses  of 
the  sun  belonged  to  the  sun  or  moon  ;  but  during  the  last  eclipse  of 
the  sun,  it  was  noticed  that  the  flames  moved  ivith  the  sun,  and  were 
gradually  covered  and  uncovered  by  the  moon  at  successive  instants 
of  the  eclipse.  Mo  one  could  doubt  thenceforth  that  they  belonged 
to  the  sun. 


I     i' 


§  sS.    THE   METHOD  OF  RESIDUES 


213 


"Whenever,  again,  plienomena  go  tlirough  Periodic  C7/^?;/j,'i'j-,  alter- 
nately increasing  and  decreasing,  we  should  seek  for  other  jihe- 
nomena  which  go  through  changes  in  exactly  the  same  periods,  and 
these  will  probably  be  a  connection  of  cause  and  effect.  It  is  thus 
that  the  tides  are  proved  to  be  due  to  tlie  attraction  of  the  moon  and 
sun,  because  the  periods  ol  high  and  low,  spring  and  neap  tides, 
succeed  each  other  in  intervals  corresponding  to  the  apparent  revo- 
lutions of  those  bodies  round  the  earth.  The  fact  that  the  moo-i 
revolves  upon  its  own  axis  in  exactly  the  same  period  that  it  revolves 
round  the  earth,  so  that  for  unknown  ages  past  the  same  side  of  the 
moon  has  always  been  turned  toward  the  earth,  is  a  most  perfect 
case  of  concomitant  variations,  conclusively  proving  that  the  earth's 
attraction  govern^  the  motions  of  the  moon  on  its  own  axis. 

"The  most  extraordinary  case  of  variations,  however,  consists  in 
the  connection  which  has  of  late  years  been  shown  to  exist  between 
the  Aurora  Borealis,  magnetic  storms,  and  the  spots  on  the  sun. 
It  has  only  in  the  last  thirty  or  forty  years  become  known  that  the 
magnetic  compass  is  sul)ject  at  intervals  to  very  sliglit,  but  curious 
movements ;  and  that,  at  tlie  same  time,  there  are  usually  natural 
currents  of  electricitv  produced  in  telegraph  wires,  so  as  to  interfere 
with  the  transmission  of  messages.  These  disturbances  are  known 
as  magnetic  storms,  and  are  often  observed  to  occur  when  a  fine  dis- 
play of  the  Northern  or  Southern  Lights  is  taking  place  in  .some 
part  of  the  earth.  Observations  during  many  years  have  shown 
that  these  storms  come  to  their  worst  at  the  end  of  every  eleven 
years.  .  .  .  Close  observations  of  the  sun  during  tliirty  o'"  forty  years 
have  shown  that  the  size  and  number  of  the  dark  spots,  which 
are  gigantic  storms  going  on  upon  the  sun's  surface,  increase  and 
decrease  exactly  at  the  same  j^eriods  of  time  as  the  magnetic  stornis 
upon  the  earth's  surface.  No  one  can  doubt,  then,  that  these  st!  .mge 
phenomena  are  connected  together,  though  the  mode  of  the  con- 
nection is  quite  unknown.  .  .  .  This  is  a  most  remarkable  and 
extensive  case  of  concomitant  variations."^ 

§  58.    The  Method  of   Residues.  —  Wo  have  said  that 

^  Jevons,  Lessons  in  l-ogic,  pp.  249-25 1. 


f 


■Mn 


214 


CAUSAL   DE TERM INATION 


4/    IK 


1 

i 

,  1' 

if 

i;J 

1! 

/ 


modern  science  employs  measurement  whenever  j^ossi- 
ble,  in  order  to  determine  exactly  the  quantitative  rela- 
tions of  phenomena.  Groups  of  facts  whose  connections 
are  at  first  not  perceived,  or  at  best  but  vaguely  appre- 
hended, are  brought  into  close  relations  with  each  other 
by  the  establishment  of  definite  quantitative  relations. 
The  knowledge  that  electricity  possesses  energy,  for 
example,  is  very  vague  and  incomplete  when  compared 
with  the  definite  equations  which  the  physicist  can  fur- 
nish between  the  electrical  current  generated  under  cer- 
tain definite  conditions,  and  the  amount  of  work  which 
it  is  capable  of  performing.  But  the  discovery  of  quan- 
titative relations  not  only  renders  our  knowledge  more 
perfect  and  complete,  it  also  enables  us  in  some  cases  to 
detect  laws  of  connection  which  would  not  otherwise  be 
observed.  We  have  already  seen  how  the  perception  of 
corresponding  changes  in  the  quantities  of  phenomena 
has  led  to  the  discovery  of  causal  laws  by  means  of  the 
method  of  Concomitant  Variations.  The  method  of 
Residues,  which  we  now  have  to  discuss,  is  also  a  method 
of  quantitative  determination. 

In  general,  this  method  calls  attention  to  any  remain- 
der or  residue  which  is  left  over  after  other  portions  of 
a  complex  phenomenon  have  been  explained.  There  are 
two  results  of  this  method  which  may  be  discussed  sep- 
arately. 

(a)  The  application  of  this  method  to  a  complex 
phenomenon  which  is  the  '  esult  of  several  causes, 
often  enables  us  to  determine  what  part  each  of  these 
causes  plays  in  the  determination  of  the  whole  fact 
under  consideration.     Mill's  fifth  canon  seems  to  apply 


§58.    THE   METHOD  OF   RESIDUES 


215 


f 


to  this  case.  It  is  as  follows  :  Subduct  froifi  any  pJic- 
}iomcnon  such  fart  as  is  known  by  previous  inductions  to 
be  the  effect  of  certain  antecedents^  and  the  residue  of  the 
phenomenon  is  the  effect  of  the  remaining  antecedents. 
Thus,  if  it  is  known  that  the  complex  phenomenon 
BAC  is  the  result  of  bac,  and  if  it  is  further  known 
that  a  is  the  cause  of  A,  and  b  of  1^,  it  follows,  of  course, 
by  subtraction  that  the  residue  still  unexplained,  C,  is 
caused  by  c,  the  remaining  antecedent. 

Of  course  the  application  of  this  method  in  concrete  cases  docs 
not  usually  resolve  itself  into  such  a  simple  process  of  subtraction. 
It  requires  work  — '  previous  inductions/  as  Mill  says  —  to  deter- 
mine wiiat  are  the  whole  number  of  antecedents  in  any  case,  as  well 
as  to  isolate  the  various  antecedents  so  as  to  determine  exactly  what 
part  of  the  eftect  is  to  be  ascribed  to  each  one.  This  may  be  illus- 
trated by  an  example  :  after  my  student's  lamp  has  been  lighted  two 
hours,  I  find  the  thermometer  has  risen  from  65^  to  70"  Fahr.  The 
phenomenon  to  be  explained  then  is  the  additional  5^  of  heat. 
There  is  no  fire,  and  it  seems  that  the  increase  in  temperature  must 
be  due  to  the  lamp,  and  the  heat  given  off  from  my  body  during 
this  period.  Suppose  that  the  lamp  i'<  burned  for  the  same  length 
of  time  while  the  room  is  unoccupied,  all  other  conditions  remaining 
the  same,  and  that  the  thermometer  shows  an  increase  of  4'  in  the 
temperature.  By  subtraction  we  could  conclude  that  the  heat  given 
off  by  the  body  on  the  former  occasion  was  the  cause  of  the  additional 
degree  of  temperature. 

To  carry  the  process  of  analysis  a  step  further.  Let  us  suppose 
that  a  half  pint  of  oil,  which  is  composed  of  hydrogen  and  carbon, 
has  been  consumed.  We  could  determine,  by  measuring  the  heat 
produced  by  the  oxidation  of  the  exact  amount  of  carbon  contained  in 
one  half  a  pint  of  oil,  what  quantity  of  heat  is  due  to  the  combustion 
of  the  carbon  contained  in  the  oil,  and,  by  subtraction,  what  must  be 
ascribed  to  the  burning  of  the  hydrogen. 

(/;)  The  second  case  in  which  this  method  may  be 


i 


J'  m 


\\ 


'I  •< 


r' 


nr 

A 

ac 


mamm 


1 

M 

! 

ii ' 

'^ 

; 

! 

1  ' 

; 

-I 

. 

«■ 

2l6 


CAUSA L  D E TK R M 1  NATION 


applied  is  where  there  is  an  unexplained  remainder  or 
residue  left  over  after  the  result  of  all  the  known  causes 
has  been  calculated.  Mill  does  not  distinguish  between 
such  instances  and  the  method  of  simple  subtraction 
discussed  above.  Since,  however,  the  cause  must  ex- 
plain the  whole  of  the  effect,  the  method  of  residues 
enjoins  us  to  continue  the  search  for  explanation. 
W/un  any  part  of  a  complex  phciiouicnon  is  still  un- 
explained by  the  causes  which  have  been  assigned,  a 
further  cause  for  this  remainder  must  be  sought  If,  for 
example,  it  were  found  by  actual  measurement  that  the 
heat  produced  by  the  lamp,  and  by  the  body  of  the 
occupant,  were  not  sufficient  to  account  for  the  change 
in  temperature  of  the  room,  it  would  be  necessary  to 
seek  for  some  further  cause  to  account  for  this  unex- 
plained remainder. 

This  method  can  scarcely  be  said  to  be  more  than 
a  demand  for  complete  and  precise  explanation.  The 
attempt,  however,  to  account  for  unexplained  resi- 
dues has  led  to  many  extremely  important  discoveries 
in  science.  Residual  phenomena  are  often  so  obscure, 
and  appear  so  uninteresting  and  unimportant  to  the 
ordinary  mind,  that  they  are  passed  over  without  ex- 
planation. It  usually  requires  the  eye  of  a  scientific 
genius  to  see  the  importance  of  things  which  appear 
trivial  and  unessential.  With  Darwin,  facts  which  might 
appear  to  an  ordinary  observer  mere  unimportant  ex- 
ceptions, were  made  the  object  of  special  attention,  and 
often  served  as  starting-points  for  his  investigations. 
Francis  Darwin,  speaking  of  his  father,  says  :  **  There 
was  one  quality  of  mind  which  seemed  to  be  of  special 


^^  5>^- 


Till':    METHOD   OF   RESIl)li:s 


217 


f 


and  extreme  advantage  in  leadin<;-  him  to  make  discover- 
ies. It  was  the  power  of  never  letting  ex'ceptions  pass 
unnoticed.  ...  A  point  apparently  slight  and  uncon- 
nected with  his  present  work  is  passed  over  by  many 
a  man  almost  unconsciously,  with  some  half-considered 
explanation,  which  is  really  no  explanation.  It  was  just 
these  things  that  he  seized  upon  to  make  a  start  from."  ^ 

Among  the  many  important  discoveries  which  have  resulted  from 
the  investigation  of  some  obscure  and  seemingly  unimportant  fact, 
we  may  mention  that  of  ozone.  It  had  been  observed  for  a  long 
time  that  the  passage  of  electric  sparks  tlirough  the  air  is  accom- 
panied by  a  peculiar  odour.  This  odour  was  also  found  near 
electrical  machines,  and  was  known  as  the  '  electrical  smell.'  No 
one  seemed  to  have  attached  any  importance  to  it  or  to  have  attempted 
to  explain  it  in  any  way,  until  Friedrich  Schtinbein,  a  professor  of 
chemistry  at  Basel,  turned  his  attention  to  the  subject.  The  result 
of  his  investigations  was  the  discovery  of  ozone,  the  peculiar  modili- 
cation  of  oxygen,  which  was  the  cans;*  Mf  the  odour. 

Another  very  striking  example  of  the  application  of  this  method 
is  afforded  by  the  history  of  the  discovery  of  thr^  planet  Ne])tune. 
In  1781  a  new  planet  was  discovered  moving  Cu  "de  all  the  other 
planets  by  Sir  William  Herschel.  This  was  the  planet  Uranus. 
When  its  orbit  came  to  be  calculated,  it  was  found  that  it  did  not 
move  as  it  might  be  expected  to  do  according  to  the  theory  of  gravi- 
tation. That  is,  the  attraction  of  the  sun  and  the  known  planets  did 
not  account  for  the  path  it  took :  it  moved  outwards  into  space 
further  than  it  ought  to  have  done.  It  was  evident  that  either  some 
mistake  must  have  been  made  in  the  observation  of  the  astronomers, 
or  some  unknown  body  must  be  dragging  it  out  of  its  course.  No 
traces  of  any  such  planet  could  be  perceived,  and  the  problem 
remained  unsolved.  In  1843,  a  student  of  St.  John's  College, 
Cambridge,  named  Adams,  undertook  to  work  out  the  movements 
of  Uranus,  to  discover,  if  possible,  the  position  of  the  body  which 


m 


1  Li/e  and  Letters  of  Charles  Danuin,  Vol.  T.  p.  125. 


:i8 


CAUSAL   DE'rERMIXATION 


/ 


I'i) 


:  ;  ! 


li  i 


was  pulling  it  out  of  what  would  otherwise  be  its  proper  path,  the 
attractions  exercised  by  the  sun  and  the  planets  in  their  different 
positions,  and  to  show  what  effect  they  would  have  in  determining 
the  orbit  of  Uranus.  Whenever  the  planet  was  deflected  outwards. 
it  was  necessary  to  show  where  the  body  was  situated  which  was 
thus  influencing  it.  In  1845  he  was  able  to  send  a  paper  to  the 
astronomer  royal  at  Greenwich,  informing  him  in  what  quarter  of  the 
heavens  the  new  planet  should  be  observed.  Wlien  the  discovery 
was  afterwards  made,  it  was  proved  that  his  calculations  were  almost 
exactly  correct.  A  failure  on  the  part  of  the  astronomer  royal  to 
cooperate  by  looking  through  his  telescope  for  the  planet  gave  the 
prior  right  of  discovery  to  a  Frenchman  named  Leverrier.  The 
latter  worked  out  his  calculations  in  the  same  way  as  Adams,  and 
obtained  almost  exactly  the  same  results.  He  sent  these  results  to 
Professor  Galle  of  the  Berlin  University  on  the  23d  September, 
1846,  asking  him  to  look  in  the  part  of  the  heavens  which  he 
indicated.  That  same  evening,  by  following  out  the  directions,  the 
planet  was  discovered  in  almost  the  exact  spot  predicted.^ 

The  history  of  this  discovery  illustrates  as  well  several  methods 
and  processes  which  we  have  not  yet  discussed,  such  as  the  forma- 
tion and  verification  of  hypotheses.  It  is  also  interesting  as  showing 
how  reason  is  able  in  certain  conditions  to  anticipate  perception. 
The  relations  and  forces  of  the  heavenly  bodies  had  been  so  per- 
fectly formulated  in  the  law  of  gravitation  that  these  two  investi- 
gators, working  in  their  studies,  were  able  to  predict  not  only  the 
presence  but  the  exact  position  of  a  planet  which  up  to  that  time  had 
never  been  observed. 


In  connection  with  Chapters  XV.  and  XVI.,  the  student  is  ad- 
vised to  read  Mill,  Log/c;  Bk.  III.  Chs.  VIII.  and  IX. 

^  Cf.  Gierke,  ,/  Popular  History  of  Astronomy  during  the  Nineteenth 
Century^  pp.  96  ff.  ;  Buckley,  A  Short  History  of  Natural  Scienre^  pp. 
302  ff. 


/ 


CHAPTER    XVII 

METHODS    OF    EXPLANATION 

Incomplete  Explanation.  —  Analogy 

§  59.  Explanation  by  Analogy.  —  \Vc  have  now  passed 
from  the  field  of  observation  to  that  of  explanation. 
Scientific  observation,  aided  by  experiment,  as  we  have 
seen,  has  to  determine  the  exact  nature  of  the  facts  of 
experience,  and  the  order  in  which  those  facts  are  con- 
nected. Explanation,  on  the  other  hand,  undertakes  to 
furnish  reasons  why  the  facts  are  as  we  find  them  to  be. 
But,  as  has  already  been  pointed  out  (§§  48,  49),  no  hard 
and  fast  line  can  be  drawn  between  the  determination 
of  the  nature  and  connection  of  facts,  and  their  explana- 
tion. The  task  which  our  thought  is  called  upon  cO 
perform  is  to  transform  obscurely  known  and  isolated 
facts  into  an  orderly  and  consistent  system  of  know- 
ledge. And,  to  accomplish  this,  it  is  necessary,  in  the 
first  place,  that  the  facts  shall  be  thoroughly  analyzed 
and  carefully  examined ;  and,  secondly,  that  they  shall 
be  grouped  together  according  to  some  general  principle 
or  principles  wliich  shall  make  clear  and  intelligible  the 
relations  in  which  they  stand  to  each  other. 

To  explain,  then,  is  just  to  show  that  some  fact  or 
group  of  facts  is  related  to  some  other  fact  or  group  with 
which  we  are  acquainted.     So  far  as  the  methods  we  have 

219 


(3//*A 


I  ii 


i 


»•  ! 


.il      • 


•in 


./ 


rnmmmt 


SR 


mm 


230 


ANAI.OGY 


!!ir  1 


discussed  cnnblc  us  to  establish  connections  between 
events,  they  may  fairly  claim  to  be  methotls  of  explana- 
tion. Nevertheless,  although  the  difference  between 
these  methods  and  those  of  explanation  proper  is  one  of 
degree  rather  than  of  essential  nature,  it  is  important  to 
keep  it  in  mind.  The  canons  which  were  stated  in  the 
last  two  chapters  —  what  Mill  named  the  experimental 
methods  —  are  rules  for  determining  the  order  and 
succession  of  particular  facts.  The  problem  before  us 
in  those  chapt  ;rs  was  to  determine  what  particular 
phenomena  of  our  experience  are  essentially  and  neces- 
sarily connected  as  antecedents  and  consequents.  And 
for  this  purpose  active  observation,  aided  by  experi- 
ment, suffices.  It  is,  of  course,  true  that  these  observa- 
tions and  experiments  furnish  the  starting-point  for 
explanation.  l?ut  they  constitute  a  more  or  less  distinct 
step  in  the  work  of  systematization  which  is  carried  on  by 
thought.  The  method  of  Difference,  for  instance,  enables 
us  to  say  that  hot  water  will  break  thick  glasses  when 
poured  into  them,  but  will  not  injure  thin  ones.  *  So 
much  for  the  fact,'  we  say,  'but  the  explanation  is  still 
wanting.'  We  must  try  to  make  the  fact  intelligible  by 
going  outside  of  it,  and  showing  that  this  behaviour  on 
the  part  of  the  glasses  is  simply  a  case  or  illustration  of 
what  we  already  know  of  the  properties  of  bodies  when 
heated.  Again  the  method  of  Concomitant  variations, 
as  we  have  seen  from  Jevons's  example,  has  led  us  to 
believe  in  some  causal  connection  between  electrical 
storms,  sun-spots,  and  the  Aurora  Borealis.  In  this 
instance,  knowledge  has  not  been  able  to  advance 
beyond   the  fact  to   its   explanation.     No    satisfactory 


§  59-     KXl'L.V.N  >.\    I5V    AXAL()(;Y 


221 


theory  lias  yet  been  cstablislicd  to  account  for  the 
undoubted  tact  that  tliese  i)lienonicna  are  in  some  way 
causally  connected. 

In  discussing;  methods  of  ICxplanation,  we  deal  first 
with  Analogy.  The  principle  of  Analogy  is  resem- 
blance. The  phenomenon  to  be  explained  is  connected 
with  some  more  familiar  occurrence  through  some 
perceived  or  imagined  likeness  between  the  two  cases. 
In  the  early  stages  of  the  history  of  the  race,  everything 
was  explained  on  the  analogy  of  human  actions  (cf.  §  84). 
All  natural  events,  that  is,  were  sui)i)osed  to  'l)e  produced 
by  superhuman  agents,  who  were,  however,  endowed 
with  essentially  the  same  qualities  as  man.  In  the 
thunder,  the  men  of  a  primitive  age  heard  the  voice  of  a 
god.  An  eclipse  of  the  sun  or  moon  was  interpreted  as 
a  divine  sign  or  warning.  When  the  sea  became  tem- 
pestuous and  lashed  its  shores,  they  believed  that  the 
sea-god  was  angry.  In  every  case,  they  interpreted 
these  mysterious  happenings  of  nature  by  referring 
them  to  causes  similar  in  character  to  those  which  they 
be^:t  understood  —  the  motives  and  volitions  of  them- 
selves and  their  fellows. 

The  principle  of  analogy  is  employed  in  the  same 
way  in  modern  times.  It  is  true  that  we  no  longer 
think  that  natural  events  are  directly  caused  by  the 
action  of  some  spiritunl  agent  more  or  less  like  our- 
selves. But,  when  we  endeavour  to  show  that  the  phe- 
nomena which  we  are  interested  to  explain,  are  similar 
in  important  respects  to  some  group  of  facts  with  whose 
mode  of  operation  we  are  familiar,  we  proceed  by  anal- 
ogy.    On  the  basis  of  this  similarity,  we  argue  that  the 


t.  nil 


ry 


->'>'> 


ANALOGY 


1.1   '  I 


phenomena  with  which  we  arc  deahn*;  probably  have 
the  satne  proi)erties,  or  operate  in  the  same  way,  or  a-e 
j^overnecl  by  the  same  huvs,  as  the  belter-known  facts 
which  tiiey  resemble.  The  formula  of  analogy  is 
stated  by  Mill  in  this  way:  "Two  things  resemble 
each  other  in  one  or  more  respects  ;  a  certain  proposition 
is  true  of  the  one,  therefore  it  is  true  of  the  other."  ^ 
The  following  example  of  analogy  has  been  frequently 
used  as  an  illustration  :  — 


■i'    ! 


in^ 


"We  may  observe  a  very  u;i'eat  siniilitiule  between  this  earth 
wliicli  we  inhabit,  and  the  other  planets,  Saturn,  Jupiter.  Mars, 
Venus,  and  Mercury.  They  all  revolve  round  the  sun,  as  the  earth 
does,  allhoui^h  at  different  distances  and  in  different  periods.  They 
borrow  all  their  li<;ht  from  the  sun,  as  the  earth  does.  Several  of 
them  are  knov.n  to  revolve  around  their  axes  like  the  earth,  and  by 
that  means  must  have  a  like  succession  of  day  and  night.  .Some  of 
them  have  moons  that  serve  to  give  them  light  in  the  absence  of  the 
sun,  as  our  moon  does  to  us.  They  are  all  in  their  motions  subject 
to  the  same  law  of  gravitation  as  the  earth  is.  F'rom  all  this  simili- 
tude, it  is  not  unreasonable  to  think  that  those  planets  may,  like  our 
earth,  be  the  habitation  of  various  orders  of  living  creatures." - 

The  word 'analogy' at  the  present  time  is  somewhat  loosely  used 
for  any  mark  of  similarity  or  resemblance  which  enables  us  to  reason 
from  one  thing  to  another.  "The  original  word  dvaAoyt'a,  as 
employed  by  Aristotle,  corresponds  to  the  word  Proportion  in 
Arithmetic ;  it  signifies  an  equality  of  ratios,  l(r6Tr]<i  Xoywv :  two 
compared  with  four  is  analogous  to  four  compared  with  eight. 
There  is  something  of  the  same  meaning  in  the  technical  use  of  the 
word  in  physiology,  where  it  is  used  to  signify  similarity  of  function  as 
distinguished  from  similarity  of  structure,  which  is  called  homology  ; 
thus  the  tail  of  a  whale  is  analogous  to  the  tail  of  a  fish,  inasmuch 


i/^.^'-zV,  Bk.  III.  Chap.  XX.  §  2. 

'Reiil,  Intellectual  Poiuers  of  Man,  Essay  I.  Chap.  III. 


M^ 


;y    IS 


§60.     ANAI.OC.Y   AS   SUGCKSTIVE  OF   HVPOTIIKSES     223 

as  it  is  similarly  used  for  motion,  but  is  homolo^rous  witli  the  hiiul- 
le<;s  of  :i  quiulriiped.  A  miiu's  anus  ;ue  iioinoioi^ous  with  a  iiorse's 
fore  le;;s,  hut  they  are  not  analoj^ous,  inasmuch  as  they  are  not  used 
for  progression."  ^ 

Apart  from  these  technical  uses,  what  is  known  as 
analogical  reasoning  may,  perhaps,  be  best  lietined  as 
an  argument  from  similar  instances.  In  analogy,  we  do 
not  stop  to  work  out  a  law  of  connection  between 
phenomena  by  comparing  a  number  of  cases,  or  by 
using  any  of  the  ordinary  inductive  canons.  Hut 
finding  a  striking  resemblance  between  some  circum- 
stance—  quality,  arrangement,  function,  etc.  —  in  the 
phenomena  to  be  explained,  and  some  phenomena  with 
which  we  are  already  acquainted,  we  used  the  latter  as 
a  basis  for  conclusions  about  the  former.  Analogy  is 
thus  an  argument  from  e.\am})les  or  instances,  its  value 
depending  upon  the  real  identity  in  some  important 
aspect  of  the  cases  compared.  When,  however,  our 
thought  is  able  to  extend  to  a  new  case,  or  set  of 
cases,  some  general  law  or  principle  with  whose  opera- 
tion it  is  already  acquainted  in  other  instances,  we  have 
passed  beyond  analogy  to  complete  explanation.  In 
the  former  case,  we  argue  from  the  resemblance  of 
instances ;  in  the  latter,  the  thread  which  binds  the 
new  instance  with  the  old  is  the  identity  of  a  general 
principle. 

§  60.    Analogy  as  Suggestive  of  Explanatory  Hypothe- 
ses. —  We  have  shown  above  that  analogical  reasoning 


',    ^ 


1 

I 


1  Minto,  Lo^ic  Inductive  and  Deductive,    p.  367. 


(  - 


(( 


./,- 


i    I 


''t...  .w'HR 


224 


ANALOGY 


''  #■ 


l.lrfi    ^ 


II       ! 


I'    ) 


depends  on  the  resemblance  which  exists  between  indi- 
vidual cases  or  instances,  and  that  it  is  not  guided  by 
any  general  law  or  princii)lc.  In  the  next  section,  how- 
ever, we  propose  to  show  in  more  detail  wherein  it  falls 
short,  and  why,  taken  by  itself,  it  can  only  be  regarded 
^  as  incomplete  explanation.  Here  we  have  to  notice  the 
important  part  which  it  plays  in  suggesting  laws  and 
principles.  Although  analogy  *  sticks  in  the  particular 
instances,'  it  leads  the  mind  on  to  general  laws  and 
explanatory  theories.  It  is  thus  of  the  greatest  impor- 
tance as  a  necessary  stage  on  the  way  to  complete 
explanation. 

When  \vc  are  able  to  discover  some  general  resem- 
blance between  a  group  of  phenomena  which  we  are  in- 
terested to  explain,  and  another  group  whose  principle  of 
operation  we  already  understand,  our  thought  strives  to 
extend  the  known  principle  and  to  bring  the  new  facts 
under  it.  The  unknown  or  unexplained  facts  are  thus 
brought  under  a  known  law.  It  is  of  course  true  that 
the  application  of  the  law  to  a  new  set  of  facts  broadens 
our  conception  of  its  scope,  and  often  requires  us  to  state 
it  in  a  more  adequate  way.  Thus  the  analogy  which 
Newton  perceived  between  the  heavenly  bodies  falling 
through  space  and  the  falling  of  the  apple  towards  the 
grountl,  led  to  the  formulation  in  exact  mathematical 
terms  of  the  universal  law  of  gravitation.  Our  know- 
ledge of  the  various  functions  of  plants  —  digestion,  re- 
production, etc.  —  has  been  obtained  by  ascribing  to  the 
various  organs  of  the  plant,  purposes  analogous  to  those 
which  are  fulfilled  by  the  parts  of  animal  bodies.  And, 
in  turn,  the  study  of  plant  physiology  has  thrown  light 


en  indi- 
ided  by 
m,  how- 
n  it  (alls 
egarded 
)tice  the 
aws  and 
articular 
iws  and 
t  impor- 
:omplete 

1  resem- 
e  are  in- 
iciple  of 
trives  to 
ew  facts 
are  thus 
rue  that 
jroadens 
to  state 
Y  which 
s  fallinGf 
irds  the 
miatical 
r  know- 
:ion,  re- 
::  to  the 
;o  those 
And, 
n  liijht 


§60.     ANALO'oY   AS    SUGGESTIVI':   OF    IIVI'UTIIESLS     225 

upon  animal  physiology,  and  enlarged  and  modified  many 
of  its  theories. 

An  extremely  interesting  instance  of  the  part  wliich  analogy 
plays  in  suggesting  possible  explanations,  is  found  in  the  account 
of  the  discovery  of  the  principle  of  Natural  Selection  given  Ijy  Dar- 
win in  his  Autobiography.  In  1837  Daiwin  opened  a  note-book 
for  the  pui'pose  of  record!.. «^  all  Hicts  in  any  way  connected  with  the 
variation  of  species  in  nature  ami  untler  domestication,  lie  first 
investigated  the  variations  of  plants  and  animals  whi^are  produced 
under  domestication,  by  i)rintetl  enciuiries,  by  C()l^'i>:ation  with 
sk'liul  In'.eders,  and  by  extensive  reading.  '•  1  soon  found,"  he  says, 
''  that  selection  was  the  keystone  of  man's  success  in  making  useful 
races  of  plants  and  animals."  When  useful  or  jjleasing  varieties 
of  plants  or  animals  occur,  the  gardener  or  breeder  preserves  them, 
and  their  peculiar  cjualities  are  transmitted  to  their  oflspring.  And, 
in  a  number  of  generations,  these  qualities  become  more  pronounced 
through  accumulation.  Tlie  differences  between  varieties  of  the 
same  species  of  domesticated  animals  —  varieties  whi.h  areas  dhler- 
ent,  for  example,  as  the  mastiff  and  Skye  terrier  —  are  due  to  the 
selective  agency  of  man.  Ikit  is  there  anything  analogous  takes 
place  on  an  indefinitely  larger  scale  in  nature  ?  If  so,  what  is  it 
which  ])lays  the  part  of  the  gardener  or  breeder,  and  preserves  cer- 
tain varii;ties? 

When  r3arwin  had  reached  this  point  in  his  investigations,  and 
had  come  to  apjireciate  what  selection  could  do,  he  hajjpened  to 
read  Malthus's  book,  O//  Population.  The  purpose  of  this  book 
was  to  dispel  tlie  optimistic  ideas  of  some  of  the  writers  of  the 
eighteenth  century  who  looked  for  the  speedy  realization  of  social 
well-being  and  hapjiiness.  Such  an  ideal  is  impossible  of  fulfilment, 
said  Malthus.  because  of  the  inevitable  tendency  of  population  to 
increase  faster  than  the  supply  of  food.  Human  beings  increase  in 
a  geometrical  ratio;  the  means  of  subsistence,  at  best,  only  by  an 
arithmetical  ratio.  The  poi)ulation  will  thus  constantly  tend  to 
exceed  the  limit  of  the  food  supply,  and  will  be  kept  in  check  only 
by  starvation.     A  constant  struggle  for  food  is  the  lot,  then,  to 


•I  I 


liiH 


'I       1   M 


I  ■  r  I 

1     III 


V 


226 


ANALOGY 


•;*i 


which  each  individual  's  doomed  in  virtue  of  this  law.  Darwin's 
observations  of  the  rate  r.t  wliich  plants  and  animals  tend  to  repro- 
duce their  kind,  led  him  at  once  to  extend  Malthus  s  principle  to 
the  wJiole  of  nature.  The  fecundity  of  natural  beings  leads  to  a 
struggle  for  e.\istence,  not  merely  among  men,  but  throughout  the 
whole  organic  world.  And  if  tliere  is  a  struggle,  we  have  natural 
;election  or  the  survival  of  the  fittest.  Darwin  saw  "that  natural 
selection  was  the  inevitable  result  of  the  rajMd  increase  of  all  organic 
beings.''  It  is  not  difficult  to  see  that  this  discovery  was  the  result 
of  Darwin's  wonderful  power  of  perceiving  analogies  between  differ- 
ent classes  of  facts.  His  genius  led  him  to  recognize  first  the  re- 
semblance of  the  variations  of  species  in  nature,  to  the  more  familiar 
variations  which  go  on  among  don-  _sticated  plants  and  animals. 
And,  secondly,  he  perceived  that  the  competition  for  the  means  of 
subsistence,  which  the  pressure  of  population  imposes  upon  the  mem- 
bers of  the  human  race,  is  rimply  one  phase  of  •  the  struggle  for 
existence,'  which  is  going  on  everywhere  throughout  the  organic 
world. 

§  6i.    The  Incompleteness  of  Analogical  Reasoning. — 

The  most  striking  feature  of  analogical  argimients  is 
found  in  the  fact  that  they  yield  only  probable  conclu- 
sions. And  the  reason  for  this  is  not  far  to  seek.  For, 
as  has  been  already  shown,  analogy  is  a  method  of 
reasoning  from  one  parKcular  case  to  another  on  the 
basis  of  some  imagined  or  perceived  similarity  between 
the  two  cases.  Complete  logical  demonstration,  or  cer- 
tainty, however,  is  attained  only  when  the  new  fact  or 
group  of  facts  is  really  and  essentially  united  by  means 
of  some  general  principle  with  what  is  already  known. 

But  it  must  not  be  forgotten  that  '  probability '  is  not 
a  fixed  quantity.  An  a"gument  from  analogy  may  have 
any  degree  of  v^alue,  from  zero  almost  up  to  the  limit 
of    complete   logical    certainty.      To  fully   explain   or 


§  6i.     INX'OMPLETEXESS  OF   ANALOGICAL   REASONING     22/ 

demonstrate  any  fact,  we  are  obliged,  I  think,  to  go 
beyond  analogy,  and  to  verify  its  conclusions  by  a 
method  which  has  still  to  be  described.  It  is  evident, 
nevertheless,  that  the  value  of  an  analogical  argument 
will  depend  upon  the  nature  of  the  resemblance  which 
is  taken  as  the  basis  of  inference.  In  general,  it  is 
true  that  the  greater  the  resemblance  between  the  two 
cases,  the  more  certainly  can  we  reason  from  one  to  the 
other.  This  is  not  to  say,-  however,  that  the  value  of 
the  conclusion  is  in  d'^ect  proportion  to  the  number 
of  points  of  resemblance  which  can  be  discovered.  For 
example,  we  might  reason  :  These  two  men  are  of  the 
same  height,  of  the  same  age,  live  in  the  same  house, 
come  from  the  same  town  ;  the  one  man  stands  well 
in  his  classes,  therefore  the  other  probably  does  so  also. 
If  the  number  of  points  of  resemblance  were  the  essen- 
tial thing,  the  argument  ought  to  possess  some  weight, 
but  it  is  clear  that  it  has  none.  The  difficulty  is  that 
none  of  the  resemblances  mentioned  are  fundamental, 
or  in  any  way  essential  to  the  real  nature  of  the  things 
compared.  If  we  knew  that  the  two  men  were  similar 
in  character,  this  cne  characteristic  would  be  worth 
more,  as  a  basis  for  the  conclusion,  than  all  the  circum- 
stances which  we  have  mentioned  combined. 

It  is  true,  then,  as  Mr.  Bosanquet  remarks,  that  in 
analogical  reasoning  we  must  iveigJi  the  points  of  re- 
semblance rather  than  couni  them.^  Other  things 
being  equal,  the  more  points  of  resemblance  we  can 
make  out  the  better :  but  if  these  are  to  contribute  at 


\ri 


n 


i 


'1-    I  ■ 


111      ■'   "H 


< ; '  !  k  ^ 


1  Logic,  Vol.  IL,  p.  99. 


§ 

ft 

' 

a 


liil,     I    -V 


228 


ANAU.tGY 


all  to  the  certainty  of  the  conclusion,  they  must  rep- 
resent some  deep-lying  characteristic  of  the  things 
compared.  In  general,  it  must  be  said  that  it  is  onlv 
experience  which  can  inform  us  what  resemblances  are 
fundamental,  and  what  merely  external.  Systematic 
knowledge  in  any  field  enables  us  to  separate  the  essen- 
tial from  the  accidental.  And,  what  is  perhaps  a  corol- 
lary from  this,  it  must  not  be  forgotten  that  the  value 
of  an  inference  from  analogy  depends  largely  upon  the 
amount  of  intellectual  insight  possessed  by  the  mind 
which  makes  it.  The  ordinary  mind,  at  least  in  its 
undisciplined  and  untutored  condition,  regards  all  things 
as  of  equal  importance.  It  is  therefore  led  away  by 
the  strongest  stimulus  —  by  striking  external  and  acci- 
dental resemblances.  On  the  other  hand,  a  scientific 
genius  whose  mind  is  well  stored  with  facts,  and  who 
is  gifted  in  addition  with  imagination,  is  able  to  pene- 
trate beneath  the  surface  and  to  apprehend  the  real  or 
fundamental  resemblance.  His  imagination  enables 
him  to  see  beyond  the  chaos  of  the  particular  facts, 
and  to  detect  the  underlying  principle  by  means  of 
which  these  facts  can  be  connected  and  systema- 
tized. 

Analogy  thus  becomes  deepened  until  it  passes  from 
the  stage  of  a  mere  argument  from  particular  to  par- 
ticular, to  the  perception  of  a  general  law  which  includes 
the  individual  instance.  But  no  such  direct  insight  can 
claim  the  title  of  knowledge,  until  it  is  tried  and  tested 
by  the  facts.  The  guesses  of  scientific  men  unfortu- 
nately often  prove  mistaken.  It  is  always  necessary 
that  fancy  shall  be  confronted  with  facts.     Even  Dar- 


§  6i.     IXCOMPLETENESS   OF   ANALOGICAL    REASONING     229 

win's  magnificent  analogical  inference  was  nothing 
more  than  a  hypothesis,  as  he  himself  well  under- 
stood, until  its  power  of  explaining  the  facts  of  organic 
life  was  demonstrated.  We  have  now  to  explain  in 
the  next  chapter  the  methods  by  which  such  guesses 
are  tested. 

References 

J.  S.  Mill,  Logic,  Bk.  III.  Ch.  XX. 

A.  Bain,  Logic,  Part  Second.  Induction,  pp.  140-148. 
J.  G.  Hibhen,  Inductive  Logic,  Ch.  XIV. 

B.  Bosanquet,  Logic,  Vol.  II.  Ch.  III. 

"  "  The  Essentials  of  Logic,  \i]i.  i^^~\t,2>. 

W.  Min'.o,  /A\i^ic  Inductive  and  Deductive,  pp.  367-373. 


•  .    m\ 


',     "< 


I   "S 


h  f 

■*;* 

4 

I  _■ 

I :     ' 

^ 

«i  '  ■ 

«i 

'• 

CHAPTER   XVIII 


i!M' 


Pi;b 


METHODS  OF  EXPLANATION. — THE  USE  OF  HYPOTHESES 

§  62.  Reasoning  from  an  Hypothesis.  —  An  hypothesis 
is  a  guess  or  supposition  made  to  explain  some  fact  or 
group  of  facts.  We  have  seen  in  the  last  chapter  how 
the  mind  is  led  on  by  the  perception  of  analogies  to 
formulate  a  general  law  or  principle  of  explanation  for 
phenomena  which  were  not  previously  understood.  But 
even  when  guided  by  analogy,  a  guess  or  hypothesis  is 
only  the  beginning  of  explanation.  A  mere  hypothesis 
or  supposition  must  be  tried  by  its  capacity  to  explain 
facts,  and  in  this  way  either  verified  or  disproved. 
'  Theory  '  is  another  word  that  is  often  used  as  equiva- 
lent to  hypothesis.  Strictly  speaking,  however,  it  is 
more  correct  to  use  the  term  '  hypothesis  '  for  the  un- 
verified, or  only  partially  verified  guess,  and  to  reserve 
'theory'  for  the  hypothesis  that  has  been  more  com- 
pletely demonstrated.  This  distinction,  however,  is  not 
usually  maintained,  and  even  in  scientific  writings  the 
terms  '  theory  '  and  *  hypothesis  '  are  used  interchangea- 
bly. Nevertheless,  it  is  necessary  to  distinguish  in  some 
way  the  '  mere  hypothesis,'  or  supposition,  which  is 
quite  as  likely  to  be  false  as  true,  from  the  hypothesis 
which   has   been  established   by   proof. 

It  is  well  to  remember  that  it  is  not  only  in  solving 
scientific  problems  that  we  employ  hypotheses.     In  our 

230 


V 


\ 


§62.     REASONING    FROM    AN    HYrorilKSlS 


231 


I 


. 


ordinary  experience,  we  are  constantly  tryinj;  to  imagine 
the  most  lii<ely  explanation  ot  tacts  which  we  i:)erceive 
through  the  senses.  If,  for  example,  one  should  find  on 
returning  to  one's  room  that  a  pane  of  glass  had  been 
broken,  one  would  straightway  set  about  finding  some 
explanation  of  this  occurrence.  One  might  perhaps 
first  imagine  that  a  stone  or  something  of  the  kind  had 
been  thrown  against  it.  Acting  on  this  supposition,  one 
would  look  for  the  stone  in  the  room.  If  it  were  found 
there,  the  hypothesis  would  be  confirmed  ;  if  no  traces  of 
it  could  be  discovered,  and  if,  moreover,  on  examination 
the  glass  proved  to  be  shattered  in  a  way  that  would 
probably  not  result  from  the  projection  of  a  stone 
against  it,  our  first  hypothesis  would  have  to  be  aban- 
doned. We  should  then  make  another  guess  —  perhaps 
that  the  outside  blind  had  been  violently  closed  by  the 
wind  —  and  again  examine  the  facts  to  see  if  they  gave 
any  support  to  this  supposition.  We  are  constantly 
making  hypotheses  of  this  character  to  explain  phe- 
nomena which  we  meet  with  in  everyday  experience. 
If  we  find  a  stream  swollen,  we  conclude  that  it  must 
have  rained  in  some  part  of  the  country  drained  by 
the  stream.  If  a  man  has  typhoid  fever,  we  are  pretty 
sure  to  guess  that  he  has  been  drinking  impure  water. 
We  no  sooner  perceive  something  unusual  or  striking 
than  we  begin  to  guess  out,  as  it  were,  its  explanation. 
The  formation  of  hypotheses,  then,  is  simply  the  mind's 
response  to  the  demand  for  explanation. 

It  is  worth  noticing  that  it  is  only  unusual  or  striking  events,  or 
those  in  which  they  have  some  practical  concern,  which  attract  the 
attention  of  the  majority  of  mankind,  and  lead  them  to  form  explana- 


i 


^•■wi|i.,Liii<t  _'.m 


I  »• 


\ir 


9\i 


L 


THE   rSK   OF    IlVI'OTIIESfclS 


tory  hypotheses.  What  is  familiar,  or  of  no  practical  importance, 
does  not  usually  awaken  curiosity.  Indeed,  in  a  great  many  cases, 
such  i)hen<jmena  are  not  observed  at  all.  lUit  the  great  scientist  is 
distinguished,  one  may  say,  by  his  intellectual  curiosity.  He  tries 
to  understand  phenomena  which  the  ordinary  mind  neglects,  and 
simply  takes  for  granted.  He  has  ([uestions  in  his  mind  with  regard 
to  familiar  things  which  he  wishes  to  have  answered,  guesses  which 
he  is  desirous  of  having  proved  or  disproved.  We  have  found  it 
convenient,  in  the  preceding  chapters,  to  separate  the  description  of 
the  proces.ses  of  determining  the  nature  of  facts,  from  the  account 
of  the  methods  of  explanation.  But  it  must  by  no  means  be  sup- 
posed that  the  nature  of  facts  is  discovered  quite  independently  of 
the  influence  of  hy|jothe.ses  or  theories.  Unless  the  mind  has 
some  fjucst'on  to  answer,  or  theory  to  test,  it  is  impossible  to  see 
any  significance  in  an  experiment.  In  other  whmxIs.  every  ex- 
periment must  have  a  purpose,  and  the  purpose  is  to  get  some 
information  that  will  help  vv.i  to  answer  a  question  w  hich  we  bring 
with  us  to  the  investigation. 

In  the  actual  process  of  acquiring  knowledge,  then, 
observation  zvd  theorizing  go  hand  in  hand.  Unless  we 
go  to  nature  with  something  in  our  mind,  we  are  not 
likely  to  learn  much.  As  a  rule,  we  see  only  what  we 
look  for.  Francis  Darwin  says  of  his  father :  "  He 
often  said  that  no  one  could  be  a  good  observer  unless 
he  were  an  active  theorizer.  This  brings  me  back  to 
what  I  said  about  his  instinct  for  arresting  exceptions: 
It  were  as  though  he  were  charged  with  theorizing 
power  ready  to  flo\v  into  any  channel  on  the  slightest 
disturbance,  so  that  no  fact,  howevci'  small,  coU'd  avoid 
releasing  a  stream  of  theory,  and  thus  the  fact  became 
magnified  into  importance.  In  this  way  it  naturally 
happened  that  many  untenable  theories  occurrec'  to  him, 
but  fortunately  his  richness  of  imagiuation  was  equalled 


f 


) 


§62.     RKASOMXC.    IROM   AN    IIVPOTHF.SFS 


2^^ 


by  his  |-)o\vcr  of  judging;  and  coiKloiiinin<;  \\\c  th<)U,L;"hts 
which  occurred  to  him.  lie  was  just  to  his  theories  and 
did  not  condemn  them  unheard  ;  and  so  it  happened 
that  he  was  willini;'  to  test  what  would  seem  to  most 
people  not  at  all  worth  testin.i;.  These  rather  wild  trials 
he  called  'fool's  experiments,'  and  enjoyed  exceedin<^ly. 
As  an  example,  I  may  mention,  that  tindini^^  the  cotyle- 
dons of  J^iophytum  to  be  highly  sensitive  to  vibrations 
of  the  table,  he  fancied  that  they  migh^  perceive  the 
vibrations  of  sound,  and  therefore  made  me  play  my 
bassoon  close  to  a  plant."  ^ 

A  good  example  of  how  essential  theories  arc  for  an 
observer,  and  how  blind  he  may  be  to  what  he  is  not 
looking  for,  is  found  in  the  work  from  which  we  have 
just  quoted.  In  the  brief  autobiography  contained  in 
the  first  volume,  Darwin  tells  of  a  geological  trip  through 
Wales  which  he  took  while  a  student  at  Cambridge,  in 
company  with  Sedgwick,  the  professor  of  geology.  It 
must  be  remembered  that  this  was  before  Agassiz  had 
come  forward  with  his  theory  of  a  glacial  j)eriod  in  the 
world's  history.  Darwin  writes  :  "  We  spent  many 
hours  in  Cwm  Idvval,  examining  all  the  rocks  with  su- 
preme care,  as  Sedgwick  was  anxious  to  fmd  fossils  in 
them  ;^  but  neither  of  us  saw  a  trace  of  the  wonderful 
glacial  phenomena  all  around  us ;  we  did  not  notice  the 
plainly  scored  rocks,  the  perched  l»oulders,  the  lateral 
and  terminal  moraines.  Yet  these  phenomena  are  so 
conspicuous  that,  a.^  I  declared  in  a  paper  published 
many  years  afterward  in  the  PJiilosopliiral  Magazine,  a 


i 


\ 


1  Life  and  I rtters  of  Charles  Darxuin,  Vol.  I.,  p.  126. 


V 


house  burnt  down  by  ire  did  not  tell  its  story  more 
plainly  than  .i!a  thi.j  valley.  If  it  had  been  filled  by  a 
glacier,  the  phenomena  would  have  been  less  distinct 
than  they  now  are."  ^ 


m- 


§  63.  Formation  of  Hypotheses.  —  We  arc  now  ready  to 
consider  a  little  more  closely  the  formation  of  hypothe- 
ses or  theories.  In  the  first  place,  it  is  to  be  noticed 
that  hypotheses  are  not  received  from  without  through 
sense-perception,  but  are  made  by  the  mind.  They  are 
the  creations  of  the  imagination.  A  good  theorizer,  like 
a  poet,  is  in  a  certain  sense  born,  not  made.  The  man 
to  whom  '  nothing  ever  occurs,'  whose  intellectual  pro- 
cesses are  never  lit  up  with  a  spark  of  imagination,  is 
unlikely  to  make  any  important  discoveries.  It  has 
been  by  a  flash  of  scientific  genius,  by  imaginative  in- 
sight which  we  may  all.  'St  call  inspiration,  that  great 
scientific  theories  have  been  discovered.  Not  even  a 
scientific  genius,  however,  can  afford  to  neglect  the 
facts.  But,  guided  by  accurate  observation,  the  scien- 
tific imagination  tries  to  invent  some  law  or  principle 
which  will  serve  to  connect  and  explain  facts.  Tyndall 
has  an  essay  on  "  The  Scientific  Use  of  the  Imagina- 
tion," from  which  we  may  quote  a  short  passage. 
"  With  accurate  experiment  and  observation  to  work 
upon,  imagination  becomes  the  architect  of  physical 
theory.  Newton's  passage  from  a  falling  apple  to  a 
falling  moon  was  an  act  of  the  prepared  imagination. 
.  .  .     Out  of  the  facts   of  chemistry  the  constructive 

^  Li/c  and  Letters  of  Charles  Darwin,  Vol.  I,,  p.  49. 


I 


1 

I' 


\  4- 


§63.     rOKMATIOX    OF    nVPoiIIKSKS 


235 


imagination  ot  Dalton  formed  the  atomic  theory.  Davy 
was  richly  endowed  with  the  ima<^inative  faculty,  while 
with  i'^iraday  its  exercise  was  incessant,  preceding, 
acconipanyin^uj,  and  jj^uidinj^  all  his  exj)eriinents.  His 
strength  and  fertility  as  a  discoverer  are  to  be  referred 
in  great  part  to  the  stimulus  of  the  imagination.  Scien- 
tific men  fight  shy  of  the  word  because  of  its  ultra- 
scientific  connotations;  but  the  fact  is,  that  without  the 
exercise  of  this  power,  our  knowledge  of  nature  would 
be  a  mere  tabulation  of  coexistences  and  sequences."^ 

In  spoakiii*;  of  hypotheses  as  'guesses,'  or  'creations  of  tlie  im- 
agination." their  dependence  upon  facts  must  not  be  forgotten.  It  is 
only  when  the  phenomena  to  be  explained  have  been  carLt'ully  ol)- 
served  that  our  guesses  at  their  explanation  are  likely  to  be  of  value. 
It  is  well  known  that  a  considerable  anu)unt  of  knowledge  is  usually 
required  to  ask  an  intelligent  question.  And  in  the  same  way,  the 
mind  must  be  well  stored  with  facts,  in  order  to  rentier  ovu'  hypo- 
thetical explanations  worthy  of  consideration.  Indeed,  observation 
of  facts,  and  the  formation  of  theories  go  hand  in  hand,  and  naturally 
assist  each  other.  We  have  already  spoken  of  the  lack  of  theory 
which  makes  us  blind  to  Hicts  which  seem  to  lie  directly  before  us. 
Rut  we  have  perhaps  not  yet  emphasized  sufficiently  the  dependence 
of  theories  upon  the  facts  of  observation.  The  process  of  explanation 
may  be  described  as  a  fitting  together  of  the  facts  given  by  observa- 
tion, with  the  explanatory  theories  which  the  mind  originates.  The 
theory  with  which  we  start  enables  us  to  ask  questions,  and  leads  us 
to  scrutinize  the  phenomena  which  are  to  be  explained  ;  while  the 
latter  react  upon  the  theory,  and  cause  it  to  undergo  constant  modifi- 
cation. The  account  of  Darwin's  discovery  of  the  principle  of  'the 
survival  of  the  fittest '  is  a  good  illustration  of  an  hypothesis  con- 
structed by  a  constant  dependence  upon  the  facts  during  every  step 
of  its  progress. 


I'  I'  4. 


•  .    Ill  I 

■1 


I     • 


^  Fragtnetits  of  Science y  p.  104. 


B^tr-^fi' 


236 


rilH   USH  OF   IIVl'orilKSES 


\Vc  have  already  referretl  to  the  way  in  which  analoj^y 
leads  the  iiiiiul  on  to  general  principles  of  explanation 
(§  60).  Analon^y  is  a  method  of  inferring  that  what  is 
true  of  one  object  is  probably  true  of  others  which 
resemble  it.  But  the  ordinary  mind  sees  resemblances 
only  when  they  are  very  obvious  and  striking.  The  man 
of  scientific  insight,  on  the  other  hand,  like  the  poet,  i)cnc- 
trates  more  deeply  into  the  nature  of  things,  and  is  able 
to  discover  analogies  and  resemblances  to  which  the 
ordinary  man  is  blind.  Who  but  a  genius  like  Newton 
would  have  thought  of  connecting  the  fall  of  an  apple 
with  the  fall  of  the  heavenly  bodies  through  space  ?  The 
history  of  science  shows  that  great  discoveries  are 
made  by  means  of  imaginative  insight,  but  it  also 
teaches  that  mere  imagination  without  dependence 
upon  known  facts  is  frequently  a  source  of  much  mis- 
chief. Mere  theories  without  facts  are  not  only  empty, 
but  often  stand  in  the  way  of  true  knowledge.  The 
fruitful  exercise  of  the  imagination,  if  we  may  judge 
from  the  way  in  which  great  discoveries  have  been  made, 
always  takes  place  in  closest  connection  with  what  ob- 
servation and  experiment  reveal  regarding  the  nature 
of  phenomena.  If  the  imagination  is  to  have  power  to 
discover  any  truth,  it  must  constantly  '  touch  earth,' 
and  be  guided  in  its  course  by  the  nature  of  facts  which 
are  already  known. 

In  framing  hypotheses,  then,  the  imagination  is 
constantly  prompted  by  analogies  with  processes  which 
are  more  or  less  familiar.  The  hypothesis,  then,  is  not 
created  by  the  imagination  'out  of  nothing.'  It  is  rather 
an  extension  or  development  of  a  known  law,  than  an 
absolute  creation. 


I 


§64.    riiK  ruooF  OK  AN  nvroriiKsis 


'^11 


§  64.  The  Proof  of  an  Hypothesis — \Vc  luivc  discussctl 
the  way  in  wliich  hypotheses  are  formed,  l)ut  as  yet  have 
said  nothiiii;"  re^ardin;;"  tiie  means  of  determining;  tlieir 
trutli  and  lalsity.  Hut  to  form  hypotiieses  is  usually 
easy,  to  verify  them  is  ollen  exeeediuj^ly  difficult.  The 
scientific  worker  constantly  finds  that  theories  which  he 
has  formed  are  without  foundation,  and  must  therefore 
be  discarded.  It  is  not  only  essential  that  a  scientific 
investigator  shall  possess  a  mind  fertile  in  ideas  ;  he 
must  also  love  truth  more  than  any  theory,  no  matter 
how  interesting  or  attractive  it  may  appear.  In  behalf 
of  truth,  every  theory  must  be  subjected  to  the  most 
thorough  and  searching  tests  possible  ;  if  it  is  not  l)ornc 
out  by  the  facts,  it  must  be  at  once  discarded.  What 
now  is  the  general  method  of  procedure  in  testing  an 
hypothesis  .-*  Two  steps  or  stages  may  be  distinguished 
in  this  process:  (i)We  assume  that  the  hypothesis  is 
true,  and  proceed  to  show  what  are  the  necessary  results 
which  follow  from  it.  In  doing  so  we  proceed  deduc- 
tively ;  that  is,  assuming  the  truth  of  the  hypothesis, 
we  reason  out  what  consequences  it  must  have.  (2)  The 
conclusions  thus  reached  are  compared  with  the  actual 
facts,  as  given  to  us  directly  in  perception,  or  as  deter- 
mined by  experiment.  If  these  are  found  to  agree,  the 
hypothesis  is  regarded  as  true  ;  if  they  do  not  agree,  it 
must  be  discarded  or  modified. 

This  procedure  may  become  clearer  by  considering 
some  concrete  examples.  If  we  were  to  come  on  the 
campus  some  morning  and  find  that  several  branches 
had  been  broken  from  one  of  the  trees,  we  should 
naturally  try  to  explain  this    circumstance   by  makin 


1 


'Mil 


t.  II 


(r 


'tawikcM» 


H   'i 


>'    M 


!'!■ 


238 


THE    USE   OK   liVrOTIIESES 


some  hypothesis.  Perhaps  the  first  thing  which  woukl 
occur  to  us  would  be  that  there  had  been  a  violent  wind- 
storm. The  hypothesis  having  been  made,  the  next  step 
would  be  to  look  around  to  see  if  it  could  be  verified. 
'  If  there  has  been  a  cyclone,'  we  might  argue,  '  there 
should  be  other  signs  of  its  presence ;  we  should  find 
broken  twigs  and  blown  leaves  lying  about,  and  all  the 
trees  should  present  a  storm-tossed  appearance.'  If 
observation  showed  that  these  things  were  actually 
present,  we  would  consider  our  hypothesis  so  far  con- 
firmed. But  if  not,  our  first  guess  would  be  disproved, 
and  it  would  be  necessary  to  look  about  for  another 
explanation. 

An  excellent  il  :stration  of  the  way  in  which  an  hypothesis 
becomes  more  and  more  completely  demonstrated,  is  found  in  the 
history  of  the  experiments  by  which  it  was  proved  tiiat  the  atmos- 
phere has  weight,  (ialileo  noticed  that  water  will  rise  in  a  pump  only 
about  33  feet.  lie  could  not  find  out,  however,  why  it  was  that  the 
water  slioukl  stop  at  this  point.  After  his  death,  his  friend  and  puj)!! 
Torricelli  ♦ook  up  the  problem,  and  asked  himself  :  Why  does  the 
water  rise  at  all  ?  It  then  occurred  to  him  that  air  must  weigh  some- 
thing, and  that  it  might  be  this  weight  on  the  surface  of  the  water 
which  forced  the  water  up  the  i)ump  when  there  was  no  air  pressing 
it  down.  Now,  if  this  were  so,  he  reasoned,  the  weight  of  the  air 
ougnt  to  lift  mercury,  which  is  fourteen  times  heavier  than  watei,  to 
one-fourteenth  of  the  height.  So  he  took  some  mercury,  and  filling 
a  tube  about  34  inches  long,  turned  it  upside  down  into  a  basin  of 
mercury  which  was  open,  and  therefore  under  the  pressure  of  the 
atmosijhere.  The  mercury  began  to  settle  in  the  tube,  and  finally 
rested  at  a  height  of  30  inches.  Torricelli  had  thus  invented  the 
barometer,  an  instrument  which  would  measure  the  weight  of  the 
atmosphere.  It  was  afterwards  suggested  by  the  famous  French 
writer,  Pascal,  that  at  the  top  of  a  high  mountain,  where  there  is  less 


§04.     rilH    PROOF   Of   AX    IIYl'Ol'lIfSIS 


239 


1'^ 


air  pressing  downwards,  the  column  of  mercury  should  fall  consid- 
erably if  the  atmosplKTc  were  really  what  caused  the  water  and  the 
mercury  to  rise.  When  this  experiment  waj»  made  by  carrying  the 
barometer  f -i  the  top  of  a  mountain  called  the  Puy  de  Dome,  the  mer- 
cury fell  nearly  three  inches.  Still  further  confirmation  of  Torri- 
celli's  theory  was  afforded  by  the  discoveries  of  Otto  (iuericke  of 
Madgeburg.  In  1650  Guericke  invented  the  air-pump.  The  first  use 
which  he  made  of  his  new  invention  was  to  show  that  the  atmos- 
pliere  is  pressing  down  upon  us  heavily  and  ecjually  in  all  directions. 
He  litted  closely  together  two  metal  hemispheres  and  exhausted  the 
ail  between  them  by  means  of  his  pump.  It  was  tound  that  the 
pressure  of  the  atmosi)here  was  so  great  that  it  took  a  great  force  to 
separate  the  hemis|)heres.^ 

To  establish  a  scientific  theory,  then,  there  are  neces- 
sary not  only  a  ready  imagination,  but  also  patience  and 
perseverance  in  the  careful  deduction  of  the  conse- 
quences of  the  theory,  and  in  the  comparison  of  the 
results  thus  obtained  with  the  actual  facts.  Scientific 
work  also  demands  the  utmost  candor  antl  openness  of 
mind  on  the  part  ct  those  who  engage  in  it.  One  must 
be  willing  to  abandon  any  theory  as  soon  as  it  is  found 
to  disagree  with  the  facts.  And  this  is  by  no  means  an 
easy  thing  to  do.  When  one  has  a  theory  which  suffices 
for  nearly  all  the  facts,  there  is  always  a  temptation  to 
cling  to  it,  and  to  neglect  or  explain  away  any  trouble- 
some or  contradictory  facts.  There  is  no  doubt  that 
the  scientific  explanations  which  have  become  accepted 
and  established  were  not  the  ideas  which  first  happened 
to  occur  to  the  men  with  whose  names  they  are  associ- 
ated. When  Newton  first  attemjited  to  work  out  the 
verification  of  the  gravitation  hypothesis,  he  used  the 

^  Cf.  Buckley,  Short  History  of  Natural  Science,  pp.  114-121. 


in' 


I    m 


\u  I  i, 


,/ 


^r 


n 


i' 


240 


TIIK   USE  OF    IIYPOTIIKSES 


most  accurate  measurcmonts  he  coukl  ol^tain  regarding 
the  size  of  the  earth.  Ikit  in  calcuhiting  on  this  basis 
the  pull  of  the  earth  on  the  moon,  and  the  consequent 
deflection  of  the  moon  from  the  straight  line,  his  results 
came  out  wrong.  That  is,  the  moon  moved  more  slowly 
'han  it  ought  to  do  according  to  his  theory.  The  iliffer- 
ence  was  not  great,  but  Newton  could  not  overlook  this 
lack  of  agreement  with  the  observed  facts.  He  put  the 
whole  matter  aside  ;  and  it  was  only  when  he  heard 
sixteen  years  later  that  Picart  had  discovered,  from  new 
and  more  accurate  measurements,  that  the  earth  was 
larger  than  had  been  supposed,  that  he  repeated  his 
calculations,  and  found  his  hypothesis  verified. 

Although  it  very  frequently  turns  out,  both  in  every- 
day matters  and  in  scientific  work,  that  our  hypotheses 
are  disproved,  the  negative  answers  thus  obtained  are 
not  without  value.  For  we  are  often  able  at  once  to 
limit  the  number  of  possible  hypotheses.  In  a  field 
where  we  already  possess  some  systematic  knowledge,  it 
is  often  possible  to  say:  The  explanation  of  this  group 
ot  phenomena  must  be  either  a  or  /;  or  c.  If,  then,  one 
is  able  to  show  that  neither  a  nor  b  will  afford  the 
required  explanation,  these  negative  conclusions  will 
lead  directly  to  the  establishment  of  c. 

§  65.  Requirements  of  a  Good  Hypothesis.  —  Various 
conditions  or  requisites  of  a  good  hypothesis  are  laid 
down  by  writers  on  logic.  The  three  law^s  which  are 
most  frequently  stated  are  as  follows :  ( i )  That  the 
hypothesis  shall  be  conceivable  and  not  absurd.  (2) 
That  it  shall  be  of  such  a  character  that  dt^ductions 


§65.     KKQUIRKNIKNTS  OF  A  (]OOD   HYPO  Til  KSIS     24 1 


i 


can  be  made  from  it.     (3)  That  it  shall  not  contradict 
any  of  the  known  laws  of  nature. 

It  does  not  seem  to  me  that  the  first  law  is  of  much 
value.  It  is  largely  individual  taste  or  education  which 
leads  us  to  pronounce  certain  theories  '  id^surd  '  or  '  in- 
conceivable.' Thus,  for  a  long  time,  it  seemed  incon- 
ceivable that  the  earth  should  be  round,  and  should 
revolve  on  its  own  axis ;  and  less  than  a  generation 
ago  the  theory  of  evolution,  as  propounded  by  Darwin, 
seemed  to  many  persons  utterly  '  absurd.'  Nor  can  the 
third  law  always  be  applied  as  a  test  of  an  hypothesis, 
for  many  great  discoveries  seemed,  at  the  time  when 
they  were  announced,  to  contradict  known  laws  of  nat- 
ure. The  difficulty  is  that  no  one  is  able  to  affirm, 
unconditionally,  that  a  law  of  nature  forbids  us  10 
make  this  or  that  hyiK)thesis.  Of  course,  we  feel  that 
a  theory  is  very  probably  false  which  is  at  variance  with 
the  law  of  gravity,  or  with  that  of  the  conservation 
of  energy,  or  any  of  the  laws  which  we  regard  as  es- 
tablished beyond  a  reasonable  doubt.  But,  although 
the  chances  are  always  very  greatly  against  any  theory 
which  runs  counter  to  what  are  regarded  as  well-estab- 
lished laws,  there  is  yet  always  a  possibility  that  it  may 
be  true.  There  is  no  law  of  nature  so  certain  as  to  be 
infallible.  lu'en  those  laws  which  apj^ear  to  be  beyond 
the  possibility  of  doubt,  may  require  to  be  modified  or 
supplemented.  We  may  finci  tJKit,  practically,  it  is  not 
wise  to  trouble  ourselves  with  theories  which  undertake 
to  overthrow  the  law  of  gravitation,  or  to  disprove  other 
fundamental  laws  of  the  pliysical  world.  lUit  theo- 
retically, at  least,  there  is  always  a  chance  —  in  cases 

R 


,  'p 


».  Ub 


[  -1 


li.ii 


If- 


242 


THE   USE   ()E    IIVrOTlIESES 


H  i 


ill 


« 


such  as  vvc  have  been  supposing  the  chance  is  ahnost 
infinitely  small  —  that  the  new  theory  may  be  right,  and 
the  old  one  wrong.  The  practical  objection  to  admit- 
ting the  claims  of  this  canon  is  the  difficulty  in  apply- 
ing it  fairly.  The  phrase,  '  contrary  to  the  laws  of 
nature,'  like  *  inccmceivable,'  and  'absurd,'  is  likely  to  be 
used  to  condemn  any  theory  with  which  one  disagrees. 
In  this  way,  it  is  evident  that  the  very  point  is  begged 
which  is  really  at  issue. 

Of  these  three  canons,  therefore,  the  second  appears  to 
state  the  only  condition  which  is  essential  to  an  hypothe- 
sis. An  hypothesis,  if  it  is  to  be  of  any  value,  must  be 
capable  of  being  proved  or  refuted.  But,  unless  its 
consequences  can  be  shown  by  way  of  deduction,  it 
is  impossible  to  know  whether  it  agrees,  or  does  not 
agree,  with  the  facts  which  it  is  sup])osed  to  explain. 
An  hypothesis  from  which  nothing  can  be  deduced, 
then,  is  of  no  value  whatever.  It  always  remains  at 
the  stage  of  mere  possibility,  and  without  any  real 
connection  with  fact.  It  is  a  mere  guess  which  has 
no  significance  whatever,  for  it  is  entirely  incapable 
either  of  proof  or  of  disproof. 

In  general,  it  is  possible  to  deduce  the  consequences  of  a  theory 
only  when  the  principle  employed  is  analogous,  in  mode  of  oi)era- 
tion,  to  something  witli  which  we  are  familiar.  Thus,  for  example, 
it  is  because  the  ether  is  conceived  as  resembling  other  material 
bodies  in  important  respects  that  it  can  be  used  as  a  principle  of 
explanation.  It  is  assumed  to  be  elastic  and  capable  of  receiving 
and  transmitting  vibrations,  and  as  spread  out  like  other  material 
bodies  in  space.  In  virtue  of  these  similarities  to  other  material 
substances,  it  is  possible  to  deduce  the  consequences  which  such 
a  substance  as  ether  would  imply,  and  to  compare  them  with  the 


RB^LlKKMKNrS   OK    A    (iUOU    HVl'OTIIESIS     243 


actual  facts.  But  if  one  should  make  the  assumption  that  certain 
phenomena  are  clue  to  some  agency  totally  unlike  anything  of  which 
we  have  any  experience,  a  disembodied  spirit,  or  ghost,  for  example, 
it  would  be  impossible  either  to  prove  or  to  disprove  the  assertion. 
For  knowing  nothing  whatever  of  the  way  in  which  spirits  act,  one 
could  not  say  whether  the  phenomena  to  be  explained,  table-rap- 
ping, planchette-writing,  etc.,  were  or  were  not  consistent  with  a 
spirit's  nature  and  habits. 

Another  example  of  a  barren  hypothesis  from  which  no  conclu- 
sions can  be  drawn,  is  afforded  by  the  'catastroplie'  or  'convulsion' 
theory  in  geology,  which  was  first  combatted  by  Lyell.  in  his  Prin- 
ciples of  Gt'ol(\Q',  published  in  1830.  "People  h:.d  so  Vn\g  held  the 
belief  that  our  earth  had  only  existed  a  few  thuusand  years,  that 
when  geologists  began  to  find  i  great  number  of  strange  plants  and 
animals  buried  in  the  earth's  crust,  immense  thicknesses  of  rock 
laid  down  by  water,  and  whole  mountain  masses  which  must  have 
been  poured  out  by  volcanoes,  they  could  not  believe  that  this  had 
been  done  gradually,  and  only  in  parts  of  the  world  at  a  time,  as  the 
Nile  and  the  Ganges  are  now  carrying  down  earth  to  the  sea,  and 
Vesuvius,  Etna,  and  Hecla  are  pouring  out  lava  a  few  feet  thick 
every  year.  They  still  imagined  tliat  in  past  ages  there  must  have 
been  mighty  convulsions  from  time  to  time,  vast  floods  swallowing 
up  plants  and  animals  several  times  since  the  world  was  made,  vio- 
lent earthquakes  and  outbursts  from  volcanoes  shaking  the  whole 
of  Europe,  forcing  up  mountains,  and  breaking  open  valleys.  It 
seemed  to  them  that  in  those  times  when  the  face  of  the  e;^rth  was 
carved  out  into  mountains  and  valleys,  table-lands  and  deserts,  and 
when  the  rocks  were  broken,  tilted  up,  and  bent,  things  must  have 
been  very  ditVerent  from  what  they  are  now.  And  so  they  made 
imaginary  i)ictures  of  how  nature  had  worked,  instead  of  reasoning 
from  what  they  could  see  happening  around  them."^ 

The  convulsions,  or  catastrophes,  which  were  thus  assumed  to  take 
place  were  regarded  as  the  result  of  strange  incalcula!.ile  forces 
whose    mode    of    operation    could   i;ever  be   exactly   determined. 


h 


f 


''  Buckley,  Short  History  of  Xatiiral  Science^  pp.  441-442. 


1' 


244 


Till-:   USK   OK    IIYrOTllESES 


in 


Instead  of  tlicso  mysterious  aj^encies,  Lyell  assumed  that  causes 
similar  to  those  with  whicli  we  arc  now  accjuainted  had  hcen 
acting  uniformly  for  U)ng  ages.  The  natuie  of  the  causes  at  work 
being  known,  it  became  possible  to  calculate  the  nature  of  the  effects, 
and  thus  to  reduce  the  facts  of  geology  to  order  and  system.  As 
we  have  already  shown,  hypotheses  which  are  to  prove  really  service- 
able are  formed  by  extending  some  known  principle  through  analogy 
to  a  new  class  of  facts.  The  assum[)tion  of  mysteritnis  agencies 
and  principles  whose  mode  of  operation  is  unlike  anything  which  is 
known  to  us,  does  not  aid  in  the  extension  of  kno'vledge. 


t 


References 


'  ,11 


W.  S.  Jevons,  F.leincutary  Lessons  on  Lo^^ic,  Ch.  XXX. 
"     "        '<         'I/ie  J'rinii/>lcsof:Scicnce,Q\\.\X\\\. 
C.  Sigwart,  Loi^ic,  ^  83. 
B.  Dosanquet,  /^Oi^'h',  Vol.  II.,  pp.  155-167. 


4 


\  '^ 


Ml 


It  causes 
ad  been 
at  work 
ic  effects, 
em.  As 
•  service- 
analogy 
a<;encies 
which  is 


//•' 


,-^ 


/> 


CHAPTER   XIX 

FALLACIES    OF    INDUCTION 


/• 


§  6^.  The  Source  of  Fallacy.  —  It  is  necessary  at  the 
close  of  our  discussion  of  the  inductive  methods,  to  say 
something  regarding  the  errors  to  which  we  are  most 
subject  in  this  kind  of  thinking.  We  have  seen  that 
knowledge  is  the  result  of  the  mind's  own  activity,  and 
that  it  grows  in  completeness  through  a  persistent  cff(jrt 
to  keep  distinct  things  which  are  different,  and  to  con- 
nect phenomena  which  belong  together.  Truth,  in  other 
words,  is  gained  by  intellectual  activity.  And,  on  the 
other  hand,  we  fall  into  error,  and  are  led  away  by  false 
arguments  as  a  result  of  mental  indolence.  Tliinking  is 
hard  v/ork,  and  there  is  always  a  tendency  to  avoid  it.  As 
a  matter  of  fact,  we  all  think  much  less  frequently  than 
we  suppose.  Usually,  we  are  content  to  follow  familiar 
associations,  and  to  repeat  current  phrases,  without  doing 
any  real  intellectual  work.  The  difficulty  is  that  we  can 
get  along  comfortably  without  thinking  for  the  most 
part — more  comfortably,  perliaps,  than  when  we  do 
think.  Then,  again,  the  mind  is  less  directly  under  con- 
trol of  the  will  than  the  body.  One  may  force  himself 
to  sit  down  at  his  desk  and  open  a  book ;  but  it  is  more 
difficult  to  compel  oneself  to  think. 

The  only  way  in  which  we  can  be  saved  from  becom- 
ing 'intellectual  dead-beats,'  is  by  the  formation  of  good 

245 


1. 


'46 


FA  M,  AC  IKS   or   INDUCTION 


iS 


mental  habits.  It  requires  eternal  vigilance  and  unceas- 
ing strenuousness  to  prevent  our  degeneration  into  mere 
associative  machines.  What  the  logical  doctrine  of  fal- 
lacies can  do  is  to  put  us  on  our  guard  against  this  ten- 
dency. It  enumerates  and  calls  attention  to  some  of 
the  commonest  and  most  dangerous  results  of  slovenly 
thinking,  in  the  hope  that  the  student  may  learn  to 
avoid  these  errors.  Some  of  the  fallacies  of  which  we 
shall  treat  in  this  chapter,  apply  equally  to  deducllve 
or  syllop'^tic  »"  so  ung,  an.!  hav^  been  already  treated 
in  'Jhapti-t  XL  We  shall,  however,  enumerate  them 
here  age,  n  ;"  - /  ui*.  «ake  of  completeness.  It  is  conve- 
nient to  discuss  the  various  fallacies  under  the  following 
heads  :  — 


\ 


(i)  Fallacies  due  to  the  careless  use  of  Language. 

(2)  Errors  of  Observation. 

(3)  Mistakes  in  Reasoning. 

(4)  Fallacies  due  to  Individual  Prepossessions. 

§  6y.  Fallacies  due  to  the  Careless  Use  of  Language.  -  - 
The  careless  and  unreflective  use  of  words  is  a  very  fre- 
quent source  of  error.  Words  are  the  signs  or  symbols 
of  ideas;  but  the  natural  sluggishness  of  the  mind  leads 
often  to  a  substitution  of  the  word  for  the  idea.  "  Men 
imagine  that  their  reason  governs  words,  whilst,  in  fact, 
words  react  upon  the  understanding ;  and  this  has  ren- 
dered philosophy  and  the  sciences  sophistical  and  inac- 
tive." ^     It  is  much  easier  to  deal  with  counters  than 


V 


1  Bacon,  Novum  Orgaiimn,  Aph.  LIX. 


/. 


I     4 


§67.     TIIK  CAKKLKSS   USK  OK   LANGUAGE 


247 


i 


y 


with  realities.  Since  we  must  use  words  to  express  our 
thoughts,  it  is  almost  impossible  to  jirevent  them  from 
becoming  our  masters.  The  dangers  from  the  use  of 
words  has  been  well  represented  by  Locke,  from  whom 
1  quote  .he  following  passage :  — 

'•  Men  having  i)e{  >  accustomed  from  their  cradles  to  learn  words 
which  are  easily  ji;ot  and  retained.  i>el'(>re  they  knew  or  had  tVamed 
the  complex  ideas  to  whicli  they  were  annexed,  or  which  wen?  to  l)e 
found  in  the  tilings  they  were  thought  to  stand  for.  they  usually  con- 
tinue to  do  so  all  their  lives;  and.  without  taking  the  pains  neces- 
sary to  settle  in  their  minds  determined  ideas,  they  use  their  words 
for  such  unsteady  and  confused  notions  as  they  have,  contenting 
themselves  with  the  same  words  other  peopl'  ise,  as  if  their  very 
sound  necessarily  carried  with  it  constantly  t]»>  sa-  meaning.  .  .  . 
This  inconsistency  in  men's  words  when  tb  •  co.  to  reason  con- 
cerning either  their  tenets  or  their  inte^'  .^,  "anifestly  tills  their 
discourse  with  abundance  of  empty,  uniiu  'lli;'!  )le  noise  and  jar<fon, 
especially  in  moral  matters,  where  the  rd-,  lor  the  most  j)art. 
standing  for  arbitrary  and  numerous  collLclioiis  of  ideas  not  re,LCU- 
larly  and  permanently  united  in  nature,  their  bare  sounds  are  often 
only  thought  on.  or  at  least  very  obscure  and  uncertain  notions 
annexed  to  them.  Men  take  the  words  they  tind  in  use  among  their 
neitjhbours ;  and,  that  thev  mav  not  .seem  ignorant  what  thev  stand 
for,  use  them  confidently,  without  mucli  troubling  their  heads  about 
a  certain  fixed  meaning  ;  whereby,  besides  the  ease  of  it.  they  obtain 
this  advantajie  :  That,  as  in  such  discourses  thev  seldom  are  in  the 
right,  so  they  are  as  seldom  to  be  convinced  that  they  are  in  the 
wrong;  it  being  all  one  to  go  about  to  draw  men  out  of  their  mis- 
takes who  have  no  settled  notions,  as  to  dispossess  a  vagrant  of  his 
habitation  who  has  no  .settled  al)ode."  * 

(i)  In  treating  of  the  misuse  of  words,  we  mention, 
in  the  first  place,  errors  arising  from  tlie  use  of  a  word 

*  Essay  Coticrniin^i^  Iliimau  Understanding,  Hk,  III.  Ch.  X. 


li 


«.     I  t 


i       ♦' 


.\ 


I>   ) 


f  gp': 


' '   '  I 


(        1 


248 


FALLACIKS  OF  INDUCFION 


or  plirasc  in  inori'  than  one  sense.  This  is  usually 
ealled  the  fallacy  of  lujuivocation.  In  some  eases,  the 
equivocation  may  be  mere  wilful  quibbling  on  the  part 
of  the  person  propoumliiif;;  the  argument,  as  in  the 
following  example  of  Jevons  :  — 

All  criminal  actions  outjlit  to  he  piuiislicd  by  law, 

IVosecutions  for  tlicft  ate  criminal  actions, 

Therefore  prosecutions  for  theft  ou,u;ht  to  he  punished  hy  law. 

ICxamples  of  this  kind  do  not  mislead  any  one  ;  but  in 
some  instances  the  change  of  meaning  in  words  may 
not  be  perceived,  even  by  the  person  who  employs  the 
argument.     I'or  example,  one  might  reason  :  — 

It  is  rii^Iit  to  do  ;rood  to  others. 

To  assist  A  in  obtaining  office  is  to  do  him  ij;ood, 

Therelore  it  is  right  to  assist  him  in  this  way. 

Mere  the  phrase  which  is  used  equivocally  is,  'to  do 
good,'  as  will  at  once  be  perceived. 

(2)  Another  frequent  source  of  error  in  the  use  of 
words  is  found  in  what  has  been  excellently  named 
the  Question-begging  h^pithet.  As  is  well  known,  there 
is  much  in  a  name.  Epithets  like  'class-legislation,* 
'  compromise  measure,'  '  a  dangerous  and  immoral  doc- 
trine,' are  terms  freely  used  to  describe  the  measures 
or  views  of  opponents.  And,  as  it  is  always  easier  to 
adopt  a  current  phrase,  than  to  examine  the  facts  and 
draw  our  own  conclusions,  it  is  not  surprising  that  the 
name  settles  the  whole  matter  in  the  minds  of  so  many 
people.  Of  course,  the  epithet  employed  may  beg  the 
(juestion  in  favour  of  the  subject  it  is  used  to  describe, 
as  well  as  against  it.     l\)liticians  well  understand  the 


AVii 


§67.     niH   C  AKKM'.SS    USK   OK    KANdl  .\(  iK 


240 


isiuilly 
cs,  tlie 
\c  part 
in    the 


law. 

but  in 
Is  may 
jys  tlic 


'to  do 

use   of 

named 
1,  there 
;lati{)n,' 
■al  doc- 
casures 
isier  to 
:ts  and 
lat  the 
o  many 
leg  tlie 
jscribe, 
Lud  the 


importance  of  adopting  an  impressive  and  sonorous 
election  cry  to  represent  the  plank  of  their  party.  Thus, 
party  cries  like  '  honest  money,"  '  proliihition  and  prosjjer- 
ity,'  'the  people's  cause,'  etc.,  are  essentially  question- 
begging  epithets.  J'2ven  words  like  'liberty,'  'justice,' 
and  'patriotism,'  are  frequently  used  in  such  a  way  as 
to  bring  them  under  the  class  of  fallacies  which  we 
have  here  described.  Under  this  heading,  also,  may  be 
grouped  'cant'  words  and  phrases.  When  we  accuse 
a  person  of  using  cant,  we  always  im|)ly  that  he  is 
more  or  less  consciou.sly  insincere,  that  he  is  profess- 
ing opinions  and  sentiments  which  he  does  not  really 
possess.  Any  insincere  cxjiression  which  is  made  pri- 
marily for  the  sake  of  effect  may  be  rightly  termed 
cant.  It  is  not  even  necessary  that  the  speaker  should 
be  fully  conscious  of  his  insincerity.  A  man  may  easily 
deceive  himself,  and,  as  he  repeats  f.uniliar  words  and 
phrases,  imagine  himself  to  be  overflowing  with  patriot- 
ism, or  with  sympathy  for  other.s,  or  with  religious 
feeling.s. 

(3)  F'igurative  language  is  another  frequent  source  of 
error.  Of  the  various  figures  of  speech,  perhaps  meta- 
phors are  the  most  misleading.  The  imagery  aroused 
by  metaphorical  language  is  usually  so  strong  as  to  make 
us  forget  the  difference  between  the  real  subject  under 
consideration,  and  the  matter  which  has  been  used  to 
illustrate  it.  Thus  in  discussing  problems  of  mind,  it 
is  very  common  to  employ  metaphors  drawn  from  the 
physical  sciences.  Kor  example,  we  read  in  works  on 
psychology  and  ethics  of  'the  struggle  of  ideas,'  of  '  the 
balancing  and  equilibration  of   motives,*  of   'action  in 


i 


i    '  i 


<.  1 1 


^i-fi 


250 


lAM.ACII'S   Ol-    INDUCTION 


the  dinction  ol  tlic  stronf^est  niolivc,'  etc.  Anotlier 
illustration,  which  has  been  often  quoteii,  is  Carlyle's 
ar<4ument  a«;ainst  rej^resentative  ;;overnment  founded 
on  the  analogy  between  the  ruler  of  a  state  and  tiie 
captain  of  a  ship.  The  caj)lain,  ho  says,  could  never 
brin^^  the  shij)  to  port  if  it  were  necessary  for  him 
to  call  the  crew  together,  and  get  a  vote  every  time 
he  wished  to  chanp;e  the  course.  The  real  differences 
between  the  relation  of  a  captain  to  his  crew,  and  the 
executive  officers  in  a  state  to  the  citizens,  is  lost  sight 
of  by  the  metaphor.  Metaphorical  reasoning  is  simply 
a  case  of  analogy,  the  imperfections  and  dangers  of 
which  have  been  already  j^ointed  out.  It  is,  however, 
one  of  the  errors  which  it  is  most  difficult  to  avoid.  A 
hidden  metaphor  lurks  unsuspected  in  many  of  the 
words  in  common  use.  We  may  thus  ajijireciate  the 
force  of  Heine's  humorous  petition:  "May  Heaven 
deliver  us  from  the  ICvil  One,  ami  from  metaphors."  * 


% 


§  68.  Errors  of  Observation.  —  Sometimes  insufficient 
observation  is  the  result  of  a  previously  conceived  the- 
ory ;  sometimes  it  may  be  due  to  inattention,  to  the 
difficulties  of  the  case,  or  to  lack  of  the  proper  instru- 
ments and  aids  to  observation.  We  have  already  had 
occasion  to  refer  to  the  influence  of  a  theory  on  obser- 
vation (cf.  §  62).  As  a  rule,  we  see  only  those  instances 
which  are  favourable  to  the  theory  or  belief  which  we 
already  possess.  It  requires  a  special  effort  of  attention 
to  take  account  of  negative  instances,  and  to  discover  the 


; 


h  '1 


1  Quoted  by  Minto,  f  i\i;ii\  p.  373. 


cicnt 
1  thc- 
o  the 
nstru- 
y  had 
)bscr- 
ances 
ch  we 
cntion 
^cr  the 


':'! 


§6S.     KRUOUS  OF  onSKKVATION 


251 


falsity  involved  in  some  lonj^-staiuiin^  bcliot.  Indeed,  it 
perhaps  requires  (piite  as  nuieh  mental  alertness  to  over- 
throw an  old  theory,  as  to  establish  a  new  one.  This 
tenilency  of  the  mind  to  seize  upon  affirmative  instances, 
and  to  ne};iect  the  evitlenee  afforded  by  negative  cases, 
is  well  set  forth  by  Hacon  in  the  following  passage :  — 

"  The  human  undcrstandinf;,  when  any  proposition  has  been  once 
laid  down  (eillur  from  general  admission  and  belief,  or  from  the 
pleasure  it  atTords).  forces  everything;  else  to  add  fresh  support  and 
confirmation  ;    and  althouj;h  most  coj^ent  and  abundant   instances 
may  exist  to  the  contrary,  yet  either  docs  not  observe  or  despises 
them,  or  fjets  rid  of  and  rejects  them   by  some   distinction,  with 
violent  and  injurious  prejudice,  rather  than  sacrifice  the  authority  of 
its  first  conclusions.     It  was  well  answeretl  by  him  who  was  shown 
in  a  temple  the  votive  tablets  suspended  by  such  as  had  escaped  tlic 
peril  of  shipwreck,  and  was  pressed  as  to  whether  he  would  then 
recoj^ni/e  the  power  of  the  }j;o(ls ;  •  Hut  where  are  the  portraits  of 
those  who  have  perished  in  spite  of  their  vows?'     .Ml  superstition  is 
much   the  same,  whetiier  it   be   tliat  of  astrology,  dreams,  omens, 
retributive  judgment,  or  the  like,  in  all  of  which  the  deluded  ob- 
servers observe  events  which  are  fulfilled,  but  neglect  and  pass  over 
their  failure,  though  it  be  nuich  more  common.     But  this  evil  insin- 
uates itself  still   more   craftily   in   philosophy  and   the  sciences,  in 
which  a  settled  maxim  vitiates  and  governs  every  other  circumstance, 
though  the  latter  be  much  more  worthy  of  confidence,      besides, 
even  in  the  absence  of  that  eagerness  and  want  of  thought  (which 
we  have  mentioned),  it  is  the  peculiar  and  perpetual  error  of  the 
human  understanding  to  be  more  moved  and  excited  by  afifirmativcs 
than  negatives,  whereas  it  ought  duly  and  regularly  to  be  impartial ; 
nay.  in  establishing  any  true  axiom  the  negative  instance  is  the  most 
po\    rful."  ' 

The  nature  of  this  fallacy  has  been  so  well  illustrated 

^  NoTHin  Org(Xittvii,  Hk.  I.  Aph.  XI. VI. 


\% 


«.     IM 


\   •< 


% 


2C2 


FALLACIKS  (V   INDUCFK^N 


by  tlic  quotation  which  has  just  been  j^nvcn,  that  we  may 
pass  on  at  once  to  spcal<  of  other  cases  of  insufficient 
observation.  Our  (Hscussion  of  the  processes  of  reason- 
ing have  made  it  clear  how  necessary  it  is  to  observe 
carefully  and  attentively.  The  majority  of  the  false 
theories  which  have  appeared  in  science  and  in  philoso- 
phy, as  well  as  those  of  common  life,  have  arisen  from 
lack  of  observation.  The  doctrine  of  innate  ideas,  and 
the  theory  that  combustion  was  a  process  of  giving  off 
phlogiston  —  a  substance  supposed  to  be  contained  in 
certain  bodies  —  maybe  given  as  examples.  In  some 
seaside  communities,  there  is  a  belief  that  living  beings, 
both  human  and  animal,  never  die  at  flood  tide.  'They 
always  go  out  with  the  ebb,'  it  is  said.  Again,  there  is 
a  general  belief,  which  was  shared  by  such  an  eminent 
scientist  as  Ilcrschel,  that  the  full  moon  in  rising  pos- 
sesses some  power  of  dispersing  the  clouds.  Careful 
observations  made  at  the  (Greenwich  observatory  have, 
however,  shown  conclusively  that  the  moon  has  no  such 
power  as  that  supposed.^ 

Another  circumstance  to  be  considered  in  this  con- 
nection is  the  inaccuracy  and  fallibility  of  ordinary 
memory.  Every  one  must  have  noticed  how  rarely  two 
persons  agree  completely  in  the  report  which  they  give 
of  a  conversation  which  they  have  heard,  or  of  events 
which  they  have  ex[)erienced.  This  is  due  in  part  to 
diversity  of  interest  :  each  person  remembers  those  cir- 
cumstances in  which  for  any  reason  he  is  most  strongly 
interested.     Jiut,  in  addition,  it  is  largely  the  result  of 

'  Cf.  Jevons,  Priniiples  of  Science,  Ch.  XVIII. 


J 


i 

I 


'    ;  tl 


§68.     KRKORS   Ol-    (.)liSi:RVATI()N 


253 


c  may 
Ticicnt 
cason- 
bscrve 
i  false 
hiloso- 
1  from 
IS,  and 
ing  off 
ncd  in 
1  some 
bcincfs, 
'They 
here  is 
mincnt 
icr   pos- 
I^arcful 
y  have, 
lO  such 

is  Con- 
di nary 

My  two 
?y  give 
events 
)art  to 
ise  cir- 
rongly 
;nlt  of 


the  inevital)le  tendency  of  tlie  mind  to  confuse  what  is 
actually  observed,  with  inferences  made  from  its  obsei- 
vations.  The  inability  to  distinguish  between  what  is 
really  perceived,  and  what  is  inferred,  is  moat  strongly 
marked  in  uneducated  persons,  who  are  not  on  tlieir 
guard  against  this  fallacy.  An  uneducated  person  is  cer- 
tain t'o  relate,  not  what  he  actually  saw  or  heard,  but  the 
impression  which  the  events  experienced  made  upon 
him.  He  theretore  mixes  up  the  facts  perceived,  with 
his  own  conclusions  drawn  from  them,  and  with  state- 
ments of  his  own  feelings  in  the  circumstances.  A 
lawyer  who  has  to  cross-examine  a  witness  is  usually 
well  aware  of  this  tendency,  and  takes  advantage  of  it 
to  discredit  the  testimony.  The  experienced  physician 
knows  how  worthless  is  the  ilescription  of  .syini)toms 
given  by  the  ordinary  {)atient,  or  by  symi)athetic  friends, 
or  by  an  inexperienced  nurse.  The  more  one's  s\mi)a- 
thics  and  interests  are  aroused  in  such  a  case,  the  more 
difficult  it  is  to  limit  oneself  to  an  exact  statement  of 
actual  occurrences. 

But  this  tendency  is  not  confined  to  persons  deficient 
in  knowledge  and  ordinary  culture.  It  usually  ret[uires 
special  training  to  make  one  a  good  observer  in  any 
particular  field.  It  is  by  no  means  so  easy  as  it  may 
appear  to  describe  exactly  what  one  has  seen  in  an 
experiment.  If  we  know,  or  think  that  we  know, 
the  explanation  of  the  fact,  there  is  an  almost  inevita- 
ble t':ndency  to  substitute  this  interpretation  for  the 
account  of  what  has  been  actually  observed.  Recent 
psychological  investigation,  aided  by  exact  exi)erimental 
methods,    has   done   much    to    tUsentangle   tiie   data   o( 


'  1 

■ 
11 

*| 

*• 

1    1 

t)l 


254 


l<  AI,I.A(  IKS   OF    I\I)l(  HON 


¥ 


perception  from  inferences  re,i;ar(lin<;  these  data.  As 
every  one  knows  wiio  lias  practised  psychological  intro- 
sj)ection,  it  is  only  with  the  utnuist  cMfficulty,  and  after 
lon^  trainin,L;\  that  one  can  distinguish  the  actual  [)sy- 
chological  process  j)resent  to  consciousness,  from  the 
associative  and  logical  elements  which  are  bound  up 
with  them  in  our  onHnary  e.\j)crience.  The  following 
passage  from  Mill  deals  with  this  question  :  — 

*•  The  universality  of  the  confusion  between  perceptions  and  the 
inferences  drawn  from  tlieni,  aiul  the  rarity  oi  the  power  to  discrimi- 
nate the  one  from  the  other,  ceases  to  surprise  us  when  we  consider 
that  in  the  far  greater  number  of  instances  the  actual  perceptions  of 
our  senses  arc  of  no  importance  or  interest  to  us  except  as  marks 
from  which  we  infer  somethinji^  beyond  them.  It  is  not  the  colour 
and  superficial  extension  perceived  by  the  eye  that  are  important  to 
us.  but  the  object  of  wliich  these  visible  appearances  testify  the 
presence  ;  and  where  the  sensation  itself  is  inditterent.  as  it  gener- 
ally is.  we  iiave  no  motive  to  attend  particularly  to  it.  I)ut  accpiire  a 
habit  of  passing  it  over  without  distinct  consciousness,  and  going  on 
at  once  to  the  inference.  So  that  to  know  what  the  sensatit)n  ac- 
tually was  is  a  study  in  itself,  to  which  painters,  for  example,  have 
to  train  themselves  by  long-continued  stutly  and  application.  In 
things  furtiier  removed  from  the  dominion  of  the  outward  senses, 
no  one  who  has  not  had  great  exjierience  in  psychological  analysis 
is  competent  to  break  this  intense  association  :  and  when  such  ana- 
lytic habits  do  not  exist  in  the  re(|uisite  degree,  it  is  hardly  possible 
to  mention  any  of  the  habitual  juilgments  of  mankind,  from  the 
being  of  Ood  and  the  immortality  of  the  soul  down  to  the  multi- 
plication table,  which  are  not,  or  have  not  been,  considered  as  mat- 
ter of  direct  intuition."  ' 

§69.  Mistakes  in  Reasoning. — The  problem  of  the 
inductive  processes   of  reasoning  is  to  ascertain   what 

»  /.o^ir,  Hk.  V.  C"h.  IV.  §  5. 


4^ 


§69      MISTAKKS    IN    KKASoM.NC. 


255 


facts  arc  necessarily  and  essentially  connected,  and  to 
explain  this  connection.  Now,  in  order  to  distinguish 
between  chance  conjunctions  of  phenomena,  and  real 
causal  connections,  careful  and  extensive  observation, 
aided  whenever  [)ossible  by  experiment,  must  be  em- 
ployed. In  short,  to  establish  a  real  law  of  connection 
between  phenomena,  it  is  necessary  to  use  one  or  more 
of  the  inductive  methods  described  in  Chaj)ters  XIV. 
and  XV.  Hut  to  do  this  implies,  in  many  cases,  long 
processes  of  analysis  ;  the  performance  of  intellectual 
work,  which  ordinary  minds,  at  least,  have  the  tendency 
to  shirk  whenever  possible.  It  is  much  easier  to  allow 
associations  to  control  our  thoughts,  and  to  assume  that 
events  which  happen  together  in  our  experience  a  num- 
ber of  times  are  causallv  connected.  We  are  led  to 
such  a  conclusion  by  a  natural  psychological  tendencv, 
without  taking  any  thought  about  the  matter,  while 
logical  analysis  and  discrimination  recpiire  a  distinct 
conscious  effort 

The  general  name  used  to  describe  fallacies  which 
are  due  to  this  particular  form  of  mentid  sluggishness 
x'?,  post  hoc,  irgo  proptcrJioc.  Two  events  occur  in  close 
conjunction  with  each  t>thcr,  and  it  is  then  assumed 
without  further  investigation  thai  they  are  related  to 
each  other  as  cause  and  effect.      Many  popular  supcrsti- 


un 


lions,  are  examples  of  ihis  fallacy.  Some  project  be 
on  I'Viday  turns  out  disastrously,  and  it  is  inferred  that 
some  causal  relation  existed  between  the  fate  of  the 
enterprise,  and  the  day  on  which  it  was  l)egun.  Or 
thirteen  persons  sit  down  to  dinner  together,  and  some 
one  dies  b(;fore  the  year  is  out      It  is  to  be  noticed  that 


/i^*Jl 


2  56 


I'ALLACIKS  OF   INDUCTION 


t'l 


I:  i 


IB  I    I 


such  beliefs  are  sii])purte(l  by  the  tendency,  to  which 
we  referred  in  tlie  last  section,  to  observe  only  the 
instances  in  which  the  supposed  effect  follows,  and  to 
neglect  the  negative  cases,  or  cases  of  failure.  *  Fortune 
favours  fools,*  we  exclaim  when  we  hear  of  any  piece 
of  good  luck  hapj)ening  to  any  one  not  noted  for  his 
wisdom.  lUit  we  fail  to  take  account  of  the  more 
usual  fate  of  the  weak-minded.  The  belief  that  the 
full  moon  in  rising  tlisperses  the  clouds,  which  was  also 
quoted  earlier,  is  a  good  example  vt{  post  lioi\  propter  hoc. 
In  fact,  all  the  fallacies  treated  in  this  chapter,  except 
those  due  to  language,  might  quite  properly  be  included 
under  this  heading. 

A  special  case  of  this  fallacy,  to  which  attention  may 
be  cailetl  separately,  arises  from  hasty  generalization,  or 
generalization  on  an  insufficient  basis  of  fact.  There 
is  a  constant  tendency  on  the  part  of  the  mind  to  reach 
general  conclusions,  to  express  all  its  knowledge  in  the 
form  of  general  .statejiients.  Hut,  although  it  is  the 
aim  of  science  to  express  the  truth  regarding  the  nature 
of  tile  world  in  the  form  of  general  laws,  it  is  not  allow- 
able to  hurry  on  to  such  principles  without  first  making 
our  ol)servation  of  the  facts  as  complete  as  possible. 
Thus  it  is  not  unusual  to  hear  a  traveller  declare,  on 
the  basis  of  a  very  limited  experience,  that  'the  hotels 
of  some  city  or  country  pre  thoroughly  bad.*  The 
generalizations  which  are  so  frecpicntly  made  regarding 
the  j)eculiar  characteristics  of  Americans,  or  luiglish- 
men,  or  P'renchmen  are  usually  of  the  same  sort.  Con- 
clusions regarding  the  effect  of  nioral  and  political 
ton  litions,  too,  are  often  drawn  from   observations  in 


yi    i 


0  which 
;)nly  tlic 
i,  and  to 
Fortune 
ny  piece 

1  for  his 
he  moie 
that  the 
was  also 
)pter  hoc. 
r,  except 
included 


§70.  FALLACIES  DUE  TO  INDIVIDUAL  PREPOSSESSIONS    257 

a  limited  field.  Iwen  scientific  books  are  not  always 
free  from  this  error.  In  a  recently  published  psycho- 
logical study  of  the  first  year  of  the  life  of  a  cliild, 
by  the  mothjr,  it  was  explained  wiiy  a  baby  always 
sucks  its  thi.ml)  rather  than  its  fin,L:;ers.  The  exphma- 
tion  was  that  the  thumb,  bein.i;-  on  the  outside  and  pro- 
jecting outwards,  got  oftenest  into  the  baby's  mouth, 
and  so  the  habit  was  formed.  The  point  is,  tliat  the 
mother  assumed  what  she  had  observed  in  her  own 
child  to  be  true  universally.  Other  i)arents,  however, 
declare  that  their  babies  never  i)ut  the  tiuimb  inco  the 
mouth,  but  always  the  fingers  or  the  whole  hand. 


1, 


•»:h 


f    ■! 


tion  may 
'.at ion,  or 
There 
to  reach 
;e  in  the 
it   is  the 
le  nature 
ot  allow- 
making 
possible, 
dare,  on 
le  hotels 
The 
egarding 
luiglish- 
t.     Con- 
political 
It  ions  in 


§  70.  Fallacies  due  to  Individual  Prepossessions.  — 
Bacon  named  this  class  of  fallacy  "  The  Idols  of  the 
Cave."  luich  indivicUial,  as  he  represents  the  matter, 
is  shut  up  in  his  own  cave  or  den  ;  that  is,  he  judges 
of  things  from  his  own  individual  point  of  view.  In 
the  first  i)lace,  one's  inclinations  and  passions,  likes 
and  dislikes,  pervert  one's  judgment.  It  is  exceed- 
ingly (hfficult,  as  we  all  know,  to  be  fair  to  a  person 
we  dislike,  or  to  refrain  from  judging  too  leniently 
the  shortcomings  of  those  to  whom  wr  aic  wai'mly 
attached.  Again,  it  is  not  easy  to  '  oneself  in 
the  position  of  an  impartial  spectat  when  one's 
interests  are  at  stake.  "The  understa;  ling  of  men," 
says  Bacon,  "  resembles  not  a  dry  1  it,  but  admits 
some  tincture  of  the  passions  an*  .ill."  Further- 
more, each  individual  has  a  certain  personal  bias  as  a 
result  of  his  natural  disposition  and  previous  training. 
Thus  it  is  almost  impossible  for  an  individual  to  free 


n 


,/ 


-:'-^ 


258 


lAl  ;,.U  IKS   (Jl-    INDUCriUN 


t-l 


himself  from  iuili(JiKil  prejudices,  or  from  the  standpoint 
of  the  political  party,  or  the  church  in  which  he  was 
bi'ought  up.  Or  if  a  person  does  ^ivc  uj)  his  old  views, 
he  not  infrequently  is  carried  to  the  opposite  extreme, 
and  can  see  no  good  in  what  he  formerly  believed. 
Iwen  education  and  the  pursuit  of  si)ecial  lines  of 
uivestigation  may  beget  j)rejudices  in  favour  of  particr.lar 
subjects.  When  a  man  has  been  eiigaged  exclusively  for 
a  long  time  in  a  particular  field,  employing  a  particular 
set  of  conceptions,  it  is  almost  inevitable  that  he  should 
look  at  everything  with  which  he  has  to  do  in  the  same 
light.  The  mathematician's  view  of  the  world  is  annost 
sure  to  be  different  from  that  of  the  historian,  or  that 
of  the  student  of  lesthetics.  It  is  very  difficult  for  the 
physicist  to  conceive  of  any  natural  process  except  in 
terms  of  molecules  and  vibrations.  It  is  inevitable  that 
each  man  should  be  blinded  to  some  extent  by  his  own 
presuppositions.  But  to  recognize  one's  limitations  in 
thi:,  respect,  is  to  pass,  to  some  extent  at  least,  beyond 
them. 


Moreover,  each  age,  as  well  as  each  iiKJividual,  may  be  regarded 
as  govoined  laij^ely  liy  current  presupi)osition.s  and  prejudices. 
Throuj;hout  the  Middle  A,i;es,  the()lo<;ical  doctrines  and  opinion.s 
controlled  r.most  absolutely  the  oi)inions  and  beliefs  of  mankind. 
This  inrtuence,  doubtless,  still  makes  itself  felt,  but  ])eople  are  now- 
pretty  generally  awake  to  the  danijers  from  this  source.  On  tht- 
other  hand,  it  is  mon-  diflkult  to  reali/.e  at  the  pn-scnt  time  that 
it  is  not  impossible  for  prejudices  and  prepossessions  to  grow  out 
of  scientific  work.  The  success  of  modern  scientific  methttds 
has  sometimes  K-d  investi<;att)rs  to  despise  and  belittle  the  work  of 
those  who  do  not  carry  on  their  investi«i;ations  in  laboratories,  or  do 
not  weij^h  and  measure  eserythintf.     Hut  conceptions  and  nuthods 


^ 


i 


§70.  KALLACIKS  DUK  'i( )  INDIVII  H'Al.   I'RKPf^SSF.SSK  )NS    259 


.»  ( 


Standpoint 
ich  he  was 
i  old  views, 
;c  extreme, 
y  believed, 
id    lines    of 
)f  partier.lar 
.lusively  for 
a  particular 
it  he  should 
in  the  same 
idd  is  almost 
rian,  or  that 
fu- ult  for  the 
ss  except  in 
cvitable  that 
t  by  his  own 
imitations  in 
east,  beyond 


v\y  he  regarded 
iiKJ    prejudices. 
s  and  opinions 
(..fs  of  mankind, 
people  are  now 
ource.     (^n  the 
vsent   time  tlv;it 
)ns  to  jj;ro\v  out 
entitle    methods 
ittle  the  work  ot 
horatories.  or  do 
)ns  and  methods 


which  prove  useful  in  one  science  c  uinot  always  he  cm|)loye(l  profit- 
ahly  in  anotlier.  A  conception,  or  mode  of  regarding  things,  which 
has  proved  serviceahie  in  one  tiehl  is  almost  certain  to  doniin.ile  a 
whole  age,  and  iu  l)e  used  as  an  almost  universal  principle  of  t.v- 
plan.aion.  The  eighteenth  century,  for  example,  was  greati\  under 
the  iuHuence  of  mec!ianical  ideas.  Newton's  discovery  made  it  pos- 
sii;le  to  regard  tlie  world  as  a  great  machiiu.  the  parts  ot'  which 
were  all  litleil  together  according  to  the  laws  of  mechanics.  'I'his 
view  let!  to  sucii  a  \ast  extension  of  knowledge  in  the  ri-alm  of 
physics  and  astronomy,  thai  the  conceptions  upon  which  it  is  liased 
were  apiilieil  in  every  possiljle  field  —  to  psychology,  to  ethics,  to 
political  science.  The  world  itsell'.  as  will  as  religious  cn-eds  and 
political  and  social  institutions,  were  supposed  to  ha\e  hei'U  de- 
lii)erately  made  and  fashioned  1)\'  some  agi  nt.  Again,  in  these  Liter 
years  of  the  nineteenth  century  we  are  dominated  hy  the  id(.a  of 
evolution.  The  biological  notion  of  an  organism  which  grows  or 
develops  has  Ijeen  applied  in  evir\'  possible  field.  We  speak,  for 
example,  of  the  world  as  an  organism  rather  tiian  as  a  machine,  of  the 
state  and  of  society  as  organic.  And  the  same  conception  has  been 
found  useful  in  explaining  the  nature  of  human  intelligence.  It  is 
easy  for  us  to  realize  the  limitations  a  i  i;;sufficiency  of  the  notion 
of  mechanism  as  emi)loyed  l)y  the  thinkers  of  the  eighteenth  century. 
Hut  it  is  not  improhaide  that  the  twentieth  century  may  be  able  to 
see  more  clearly  than  we  are  al)le  to  do,  tlie  weaknesses  and  limita- 
tions of  the  conception  which  has  pn)ved  so  fruitful  in  this  genera- 
tion. 

References 

IJacon,  A'07'fOH  Oixniiuin.  \\)\\ .  X.\ .Will   L.X \'I II . 
Locke,  JCs.say  Concerning  Huntan  i'micrsliuuiing^  lik.  III.  Chs. 
X.  and  XI. 

J.  S.  MiE.  Logic,  Hook  V. 

A.  Bain.  Logic.  Ft.  11.  Induction.  Hk.  VT. 

J.  Fowler.  Induiti-i'c  Logic,  Ch.  \'l. 

J.  (;.  Ilibhen.  /mii/cfive  Logic,  Ch.  XVTI. 

A.  .Sidgwick,  /  allncics  [Int.  Scient.  .Seiie.s]. 


..  ii; 


.( 


PART    111.—  Till':    NATURE    OF 
TIlOUlillT 


CUAITICR   XX 


ii 


JUDGMENT    AS    THE    KLHMENTAKV    PROCESS    OF    TllOUCillT 

§71.  Thinking  the  Process  by  which  Knowledge  grows 
or  develops.  —  Loj^ic  was  defined  (^  i )  us  the  science  of 
thinkin;j;,  and  \vc  have  seen  that  the  business  of  th()U,t;ht 
is  to  furnish  the  mind  witii  trutli  or  knowledge.  Under 
what  general  concejition,  now,  shall  we  bring  thinking, 
and  what  method  shall  we  adopt  to  aid  us  in  its  investi- 
gation ?  It  is  at  once  clear  that  thinking,  the  conscious 
process  by  which  knowledge  is  built  up,  does  not  re- 
sembl<i  mechanical  processes  like  i;)ressure,  or  attraction 
and  repulsion.  It  is  more  nearly  related  to  something 
which  has  life,  like  a  plant  or  an  animal,  and  which 
grows  or  develops  from  within,  in  accordance  with  the 
laws  of  its  own  nature.  Thinking  must  be  regarded 
rather  as  a  living,  than  as  a  dead  thing,  though  it  is 
necessary  also  to  remember  that  it  is  conscious  as  well 
as  living. 

When  the  thinking  process  is  regarded  in  this  way, 
moreover,  a  method  of  })rocedure  at  once  suggests  itself. 
In  these  days  we  have  become  familiar  with  the  notion 
of  evolution  or  development,  and  the  application  of  this 

260 


OF 


V  Tuouciirr 

ledge  grows 
c  science  of 
s  of  thoii<;ht 
lire.     Under 
i<^^  thinkin^;, 
n  its  investi- 
ic  conscious 
Iocs  not  re- 
ar attraction 
:)  sonietbin^^ 
,  and   which 
ice  with  the 
be  rei^arded 
thouj^h  it  is 
:ious  as  well 

in  this  way, 
fTCCsts  itself. 
h  the  notion 
ation  of  this 


§  71.     nii:    I'KCCKSS   OI-    IIIIN'KINC. 


26  \ 


notion  has  j)rovc(l  ol  tiic  j;reatest  service  to  sci'Mice,  and 
particuhirly  to  those  science's  which  deal  with  the  phe- 
nomena of  life.  VViiat  is  characteristic  of  this  manner  of 
re^^ardini;-  thin^^s  is  the  fact  that  it  does  not  consitler  tlie 
various  phenomena  with  which  it  deals  as  fixed,  un- 
chan<;eable  thiii^s,  each  with  a  ready-made  nature  of  its 
own.  Hut  each  thinj;-  is  simjjly  a  sta^e  of  a  j)rocess,  a 
step  on  the  way  to  somethin<;  else.  And  the  relations 
of  the  various  phenomena  to  each  other,  their  connec- 
tion ami  unity  as  parts  of  the  one  process,  tome  out 
more  clearly  when  viewed  in  this  way.  In  other  words, 
by  talsin;;  a  survey  of  the  genesis  and  growth  of  thinj^s, 
we  ^aiii  a  truer  idea  of  their  nature  and  relations  than 
would  be  possible  in  any  other  way.  The  past  history 
of  any  |)hen()menon,  the  storv  of  how  it  came  to  be 
what  jt  isr,  is  of  the  j^reatest  jK)ssible  service  in  throwi!i<; 
li.L,dit  u|)()n  its  real  nature.  Now,  one  cannot  doubt 
that  this  conception  will  also  j)rove  serviceable  in  the 
study  of  \()'^\c.  That  is  to  say,  it  will  assist  us  in  ^ain- 
in<;'  a  clearer  idea  of  the  nature  of  thinkinL;,  to  conceive 
it  as  a  conscious  function,  or  mode  of  actin.L,^  which  un- 
folds or  develops  in  accordance  with  the  {general  laws  of 
or<;anic  evolution.  And  this  process  may  l)e  sujiposed 
to  go  on  both  in  the  individual,  as  his  thought  develops 
and  his  knowledge  expands,  and  in  the  race,  as  shown 
by  its  history.  Hy  adojjtiuL;'  this  notion,  we  may  hope 
to  show  also  that  there  is  no  fundamental  difference 
in  kintl  between  the  various  intellectual  operations. 
Judgment  and  Inference,  for  example,  will  appear  as 
stages  in  the  one  ititellectual  process,  and  the  relation 
between   Induction  and  Deduction  will  become  evident. 


,li|t 


'f 


I         I' 


I       • 


262      jUDOMr.vr  as  iiii:  r.i,i:\ir,NrAkv  i-kockss 


§  "]  1.    The  Law  of  Evolution  and  its  Application  to  Logic. 

—  Thr  most  slrikiii};  chanictcristic  ol  any  ori^anisin  at  a 
low  sla^o  ol  ik'VL'iopnK'iit  is  its  almost  complete  lack  ol 
structure.  An  aiiKi'ha,  lor  example,  can  scarcely  be 
said  to  have  any  structure  ;  it  is  composed  of  protoplasm 
which  is  almost  h()mo;^eneous,  or  of  the  same  character 
throu.L,diout.  Wlu'ii  we  com|)are  an  amo-ba,  h(uvever, 
with  an  animal  much  hi,i;her  in  the  scale  of  life,  i\!^., 
a  vertebrate,  a  ^^reat  difference  is  at  once  evident. 
Instead  of  the  simple,  homo^neneous  protoplasm,  the 
or^^anism  is  comj)()sed  of  |)arts  which  are  unlike  or  hete- 
rogeneous, such  as  bones,  muscles,  tendons,  nerves, 
blood-vessels,  etc.  In  Mr.  S|)encer's  lan^uaj^e,  there 
has  been  a  clKin^e  from  a  state  of  homoj^eneity,  to 
one  of  heteroi^eneity.  The  process  of  evolution  from 
the  lower  orL;anism  to  the  higher  has  brought  with 
it  a  dilTerciUiation  of  structure.  That  is,  in  the  anueba 
then'  are  no  special  or^^ans  of  sii;ht,  or  hearings  or 
digestion,  but  all  of  these  acts  seem  to  be  i)erf()rmed 
by  any  part  of  the  or,i;;inism  indifferently.  In  the 
vertebrate,  on  tiie  other  hand,  there  is  division  of 
labour,  and  a  separate  organ  for  each  of  these  func- 
tions. One  may  also  notice  that  tiie  s:ime  change  is 
observable  when  the  acts  or  functions,  performed  by  a 
lower  organism  are  compared  with  those  of  a  higher. 
The  life  of  the  amoeba  seems  to  be  limited  almost  en- 
tirely to  assimilation  and  reproduction  ;  while,  when  we 
advance  from  the  lower  animals  to  the  higher,  and  from 
the  higher  animals  to  man,  there  is  an  ever-increa.s- 
ing  complexity  and  diversity  in  the  character  of 
the  actions  j)erformed.     We  thus  see  how  the  process 


i\ 


■ss 

I  to  Logic. 

inisin  ;il  :i 
to  lack  ot 
arcoly  be 
r()t<)j)lasm 
character 

iKuvcvcr, 

life,  r.i,--., 
:    evident. 
)lasm,  the 
<c  or  hete- 
is,   nerves, 
a^e,  there 
;eneity,   to 
Lition  Ironi 
u^ht    with 
he  anueba 
carin;;-,   or 
performed 
In    the 
livision    ot 
hese  func- 

chanj^e  is 
rnied  by  a 

a  hi,<;her. 
almost  en- 
c,  when  we 
r,  and  from 
rcr-increas- 
i;iraeter  of 
hiC  process 


§  72.    rm:  law  oi   i:v;jllti()N 


-'^>3 


of  evolution  involves  differentiation  both  of  structure 
and  of  fiinition,  in  passin;^  frouj  the  homogeneous 
to    the    hetero<;ene()US. 

Hut  differentiation,  or  increase  in  diversity,  is  only 
one  side  of  the  process  of  evolution.  As  we  pass  from 
a  lower  to  a  hi^^her  sta;;e,  the  various  parts  of  an  or- 
^Mnism  are  seen  to  become  more  essential  to  each  other. 
If  certain  plants  or  low  animal  organisms  are  divided 
into  several  jjarts,  each  part  will  l;o  on  livin<;.  Its  con- 
nection with  the  other  parts  does  not  seem  to  have  been 
at  all  necessary  to  it.  Hut  when  we  are  dealinj;  with 
higher  forms  of  life,  each  part  is  seen  to  have  its  own 
particular  function,  anil  to  be  essential  to  the  other 
])arts,  and  to  the  organism  as  a  whole.  In  other  words, 
the  parts  now  become  mend)ers,  and  the  whoK*  is  not 
simj)ly  an  a_L;_i;re|^ation  of  |)arts  or  pieces,  but  is  consti- 
tuted by  the  necessary  relation  o*  the  members  to  each 
other.  The  more  hij;hly  evolved  the  whole  with  which 
we  are  dealinij.  the  more  closely  connected  and  essential 
to  each  other  are  the  various  parts  seen  to  be.  It  be- 
comes increasinj;ly  true  that  if  one  member  suffers,  all 
the  other  members  suffer  alon^  with  it. 

I'A'ohition,  then,  not  only  exhibits  a  constant  process 
of  differentiation,  and  a  constant  increase  in  the  tliver- 
sity  of  j)arts  and  organs,  but  the'X'  t^oes  alont;  with  this 
what  mi^ht  be  called  a  process  of  unification,  whereby 
the  ])arts  are  brought  into  ever  closer  and  more  essen- 
tial relation  to  one  another.  In  this  way,  a  real  or  or- 
^i^dfiic  w/ioli\  as  oi)posed  to  a  mere  di^^ii'i'i'i^c^ft',  is  formed. 
This  is  what  Mr.  Spencer  call:-,  the  process  of  integra- 
tion;  and  it  accompanies,  as  we  have  seen,  what  the 
same  writer  calls  differentiation. 


'  y 


■I 


IMAGE  EVALUATION 
TEST  TARGET  (MT.3) 


// 


^o 


:/. 


7a 


1.0     [ri'M  IIIM 


I.I 


!^  ■-  IIIM 


a^ 


11:25  III;;  1.4 


2.0 


1.6 


\ 


Photographic 

Sciences 
Corporation 


4^ 


iV 


'^ 


o 


?v 


% 


■«> 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


6^ 


K^^S^' 


*/i 


11 


w 


•ri! 


|i;f  ' 


I  H 


i 


264        JUDGMENT  AS  THE   ELEMENTARY   PROCESS 

The  application  of  this  general  law  of  evolution  to 
the  development  of  the  thinking  process  is  not  diffi- 
cult. We  shall  expect  to  find  that  thinking,  in  its 
first  beginnings,  both  in  the  individual  and  in  the  race, 
will  be  much  less  complex  than  at  a  higher  stage. 
That  is,  the  earliest  or  simplest  thinking  tends  to  take 
things  in  a  lump,  without  making  any  distinctions. 
The  infant,  for  example,  does  not  distinguish  one 
person  from  another,  or  perhaps  does  not  distinguish 
even  the  parts  of  its  own  body  from  surrounding  ob- 
jects. Now,  it  is  clear  that  intellectual  development, 
growth  in  knowledge,  must  in  the  first  place  involve 
differentiation.  What  is  complex  must  be  analyzed  or 
separated  into  its  various  parts.  Things  which  are 
different  must  be  distinguished,  and  clearly  marked 
off  from  each  other.  The  development  of  thought 
implies  then,  as  one  of  its  moments,  discrimina- 
tion or  analysis  —  what  we  previously  called  differen- 
tiation. 

The  other  moment  of  the  law  of  evolution,  integration, 
also  finds  a  place  in  the  development  of  thought,  and 
goes  hand  in  hand  with  the  former.  The  child  and  the 
uneducated  man  not  only  often  fail  to  make  distinctions 
where  these  really  exist,  but  the  parts  of  their  know- 
ledge are  fragmentary,  and  have  little  or  no  relation  to 
one  another.  The  various  pieces  of  their  knowledge 
are  like  the  parts  of  the  amoeba  —  they  may  be  in- 
creased or  diminished  without  themselves  undergoing 
any  change.  But  in  order  to  i)ass  from  a  lower  to  a 
higher  intellectual  point  of  view,  —  to  become  better 
educated,  in  a  word, — it  is  necessary  to  see  the  way  in 


CSS 

olution  to 
not  cUffi- 
[ig,   in    its 
1  the  race, 
ler    stage, 
ds  to  take 
istinctions. 
gnish    one 
distinguish 
mding  ob- 
k^elopmcnt, 
,ce  involve 
nalyzed  or 
which  are 
ly   marked 
of  thought 
discrimina- 
d  differen- 

ntegration, 
ought,  and 
ild  and  the 
distinctions 
heir  know- 
relation  to 
knowledge 
nay  be  in- 
LUidergoing 
lower  to  a 
Dme  better 
the  way  in 


§  72.     THE   LAW   OF   EVOLUTION 


265 


which  the  various  pieces  of  our  knowledge  are  con- 
nected and  depend  upon  one  another.  It  is  not  enough 
to  analyze  and  keep  separate  things  which  are  distinct, 
but  it  is  also  necessary  to  understand  how  the  various 
parts  of  our  knowledge  are  so  related  as  to  be  essential 
to  one  another.  In  other  words,  we  may  say  that  it  is 
characteristic  of  our  intelligence  to  endeavour  to  put 
things  together  so  as  to  form  a  whole,  or  system  of 
interconnected  parts.  And  the  more  completely  it  is 
able  to  do  this  (provided  that  the  process  o^  differentia- 
tion has  also  made  a  corresponding  advanc^y,  the  higher 
is  the  stage  of  development  which  has  been  attained. 
The  ideal  of  knowledge,  or  of  complete  intellectual 
development,  would  be  to  understand  the  oneness  and 
relation  of  everything  which  exists,  even  of  all  those 
things  which  seem  now  to  be  entirely  different  in  kind. 
A  knowledge  of  any  one  fact  would  then  carry  with  it  a 
knowledge  of  every  other  fact.  Or,  rather,  our  know- 
ledge would  be  so  completely  unified,  that  each  part 
would  show  the  nature  of  the  whole  or  system  to 
which  it  belongs ;  just  as  a  leaf  of  a  plant,  or  the  tooth 
of  an  animal,  is  sufficient  to  tell  the  naturalist  of  the 
wholes  to  which  they  belong. 

This,  of  course,  will  always  remain  an  ideal ;  but  it  is 
in  this  direction  that  thinking  actually  develops.  It  is 
a  step  in  advance  to  discover  the  reasons  for  any  fact 
which  one  previously  knew  as  a  mere  fact.  But,  to 
discover  the  reasons  for  a  fact,  is  to  bring  it  into  con- 
nection with  other  facts,  to  see  them  no  longer  as 
isolated  and  independent,  but  as  belonging  together 
to  one  group   or   system  of   facts.     And    the   further 


S     11' 


1 

« 

V 


n 


266        JUDGMENT   AS  THE   ELEMENTARY   PROCESS 

the  process  of  explanation  goes  on,  the  more  completely 
is  our  knowledge  unified  and   related. 

There  is,  however,  another  fact  implied  in  the  very 
nature  of  evolution,  of  which  logic,  as  well  as  the  other 
sciences,  may  take  advantage.  VVc  have  assumed  that 
the  more  complete  and  difficult  kinds  of  thinking  have 
grown  or  developed  from  simpler  types  of  the  same 
process,  and  not  from  something  different  in  kind.  It 
will  therefore  follow,  that  the  essential  characteristics  of 
the  thinking  process  may  be  discovered  in  its  simplest 
and  most  elementary  form.  It  is  found  that  all  the 
essential  functions  of  the  fully  developed  organism  are 
discharged  by  the  primitive  cell.  And  because  it  is 
easier  to  study  what  is  simple  than  what  is  complex, 
the  cell  is  taken  as  the  starting-point  in  biology.  Simi- 
larly, there  will  be  an  advantage  in  beginning  with  the 
simplest  and  most  elementary  forms  of  thinking.  What 
is  found  true  of  these  simple  types  of  thought,  may  be 
assumed  to  be  essential  to  the  thinking  process  as  such. 

§  73.  Judgment  as  the  Starting-point. — What,  then, 
is  the  simplest  form  of  thinking  ?  What  shall  we  take 
as  a  starting-point,  which  will  correspond  to  the  cell  in 
biology,  or  the  elementary  process  in  psychology  ?  To 
answer  this  question,  it  is  not  necessary  first  to  decide 
where  in  the  scale  of  animal  life  that  which  we  arc  en- 
titled to  call  thinking  actually  begins.  We  shall  not  be 
obliged  to  discuss  the  much-debated  question,  whether 
or  not  dogs  think.  Wherever  thinking  may  be  found, 
it  is  essentially  an  activity  of  the  mind.  When  it  is 
present,  that  is,  there  is  always  work  done,  something 


'm 


;s 
mpletely 

the  very 
the  other 
med  that 
cing  have 
the  same 
kind.     It 
eristics  of 
5  simplest 
It  all  the 
anism  are 
ause   it   is 
complex, 
ry.     Sirai- 
g  with  the 
icr.     What 
it,  may  be 
3S  as  such. 

hat,   then, 
ill  we  take 
the  cell  in 
logy  ?     To 
t  to  decide 
we  arc  en- 
hall  not  be 
n,  whether 
/■  be  found, 
iVhen  it  is 
something 


157^.     JUDGMENT   AS    THE   STARTING-POLVl  267 

interpreted  or  put  together,  and  a  conclusion  reached. 
One  may  perhaps  say  tliat  thinking  is  simply  the  way 
in  which  the  mintl  puts  two  and  two  together  and  sees 
f:  what  the  result  is.     It  implies  that  the  mind  has  waked 

up  to  the  significance  of  things,  and  has  interpreted 
them  for  itself.  Suppose  that  one  were  sitting  in  one's 
room  very  much  engaged  with  some  study,  or  wrapt  up 
in  an  interesting  book,  and  suppose  that  at  the  same 
time  the  sound  of  a  drum  fell  upon  one's  ears.  Now, 
the  sound  sensations  might  be  present  to  consciousness 
without  calling  forth  any  reaction  on  the  part  of  the 
mind.  That  is,  we  might  be  so  intent  on  our  book  that 
we  should  not  wake  up,  as  we  have  been  saying,  to  the 
meaning  or  significance  of  the  drum-taps ;  or  perhaps 
not  even  to  the  fact  that  they  were  drum-taps  at  all. 
But  if  the  mind  did  react  upon  the  sound  sensations, 
it  would  try  to  interpret  them,  or  put  them  together  so 
as  to  give  them  a  meaning.  As  a  result,  some  conclu- 
sion would  be  reached,  as,  for  example,  'the  drum  is 
beating ' ;  or  sufficient  intellectual  work  may  have  been 
done  to  give  as  a  conclusion,  *  that  is  the  Salvation  Army 
marching  up  the  street.'  In  any  case,  it  is  of  the  great- 
est importance  to  notice  that  the  conclusion  does  not 
come  into  our  minds  from  without,  but  that  it  is  the 
product  of  the  mind's  own  activity,  as  has  been  de- 
scribed. It  is  not  true,  in  other  words,  that  knowledge 
passes  into  our  minds  through  the  senses ;  it  is  only 
when  the  mind  wakes  up  to  the  meaning  of  sensations, 
and  is  able  to  put  them  together  and  interpret  them, 
that  it  gains  any  knowledge. 

Now,  the  simplest  form  of  such  an  act  of  thought  is 


r^4 


*'":.', 


ilJ 


^, 


i 


II 


I X  • 


268         JUDGMKNF   AS   TIIK    L-J.EMENTARV    PROCESS 

called  a  judgment.  Judgment,  we  may  say,  is  a  single 
intellectual  act  of  the  kind  we  have  described  ;  and  its 
conclusion  is  expressed  by  means  of  a  Proposition  ;  as, 
for  example,  'the  grass  is  green,'  'the  band  is  playing.' 
In  accordance  with  general  usage,  however,  we  may  use 
the  term  'Judgment'  for  both  the  act  itself  and  its 
result.  And  the  word  *  Proposition  '  will  then  denote 
the  external  expression  in  speech  or  writing  of  the 
product  of  an  act  of  judgment. 

In  our  investigation  of  the  nature  of  thought,  then, 
we  must  begin  with  Judgment.  There  are  three  things 
which  we  shall  have  to  do  :  (i)  to  endeavour  to  discover 
the  fundamental  characteristics  of  this  simple  type  of 
thinking ;  (2)  to  show  the  various  forms  which  it  as- 
sumes, or  to  describe  the  different  kinds  of  Judgment ; 
and  (3)  to  trace  the  process  by  which  Judgment  ex- 
pands into  the  more  complete  logical  form  of  Inference. 
Before  any  of  these  questions  are  considered,  however, 
it  is  necessary  to  meet  a  very  serious  objection  to  our 
whole  procedure  of  beginning  with  Judgment  as  the 
elementary  process  of  thinking. 

§  74.  Concepts  and  Judgments.  —  In  the  last  section, 
we  endeavoured  to  show  that  Judgment  is  the  elemen- 
tary process  of  thought,  and  that  with  it  all  knowledge 
begins.  This  view,  however,  may  seem  to  be  contra- 
dicted by  the  treatment  of  Judgment  usually  found  in 
logical  text-books.  Judgment,  it  is  said,  is  expressed 
by  a  proposition  ;  and  a  proposition  is  made  up  of  three 
parts,  subject,  predicate,  and  copula.  Thus  in  the  prop- 
osition, 'iron  is  a  metal,'  'iron '  is  the  subject,  'a  metal' 


1 


is  a  single 
d  ;  and  its 
sition  ;  as, 
is  playing.' 
vc  may  use 
-If  and  its 
icn  denote 
ing  of    the 

lught,  then, 
hree  things 
to  discover 
pie  type  of 
diich  it  as- 
Judgment ; 
dgment  ex- 
f  Inference, 
d,  however, 
tion  to  our 
lent  as  the 


ast  section, 
the  elemen- 
1  knowledge 
)  be  contra- 
Uy  found  in 
s  expressed 
up  of  three 
in  the  prop- 
:t,  'a  metal' 


§  74.     CONCKI'iS   AND  JUDGMENTS 


269 


the  predicate,  and  the  two  terms  are  joined  or  united  by 
means  of  the  copula  'is.'  A  Judgment  is  therefore 
defined  as  an  act  of  joining  together,  or,  in  negative 
judgments,  of  separating,  two  concepts  or  ideas.  If 
this  account  be  accepted,  it  follows  that  the  ideas  of 
which  the  judgment  is  composed  (iron  and  metal,  in 
the  example  given  above)  are  pieces  of  knowledge 
which  precede  the  judgment  itself.  And  the  act  by 
which  these  logical  ideas  (or,  as  they  arc  usually  called, 
concepts)  are  formed  must  also  be  earlier  and  more 
fundamental  than  the  act  of  judging.  It  is  therefore 
held  that  logic  should  begin  with  concepts,  which  are 
the  elements  out  of  which  judgments  arc  compounded, 
and  that  the  first  logical  act  consists  in  the  conception 
or  simple  apprehension  of  the  ideas  or  concepts  (cf.  §11). 

It  is  necessary  to  examine  this  position  very  care- 
fully. What  is  maintained  is  that  a  process  of  forming 
concepts,  or  logical  ideas,  presumably  quite  distinct 
from  the  activity  of  judgment,  necessarily  precedes  the 
latter.  I^efore  it  is  possible  to  judge  that  'iron  is  a 
metal,'  for  instance,  one  must  have  gained,  by  means  of 
Conception  or  Apprehension,  the  ideas  denoted  by  the 
subject  and  predicate  of  this  proposition.  Judgments, 
that  is,  are  made  or  compounded  out  of  something 
different  from  themselves. 

It  may  be  well  to  begin  the  defence  of  our  own 
position  by  noting  what  is  undoubtedly  true  in  what 
has  just  been  stated.  In  making  a  judgment  like  'iron 
is  a  metal,'  it  is,  of  course,  necessary  to  have  the  con- 
cept 'iron,'  and  the  concept  'metal.'  But  what  is 
implied   in    having   a   concept    of   anything  .-*      Let    us 


It 


li. 


i   f' 


1. 


I    ;"V      I 


i  ■    ill/ 

I  'I 


^I'l^* 


'  I 


;2 


t  'I        li 


«i«»Mfcae*J*»  mtamt  d 


(, 


K     E:l 


ri 


It 


1   1 


li  '"'I 


ll 


mi 


il\ 


a 


I 


,i'! 


270        JUDdMKNT   AS   THE    ELEMKNTARV    PROCESS 

suppose  that  a  person  is  making  the  above-mentioned 
judgment  for  the  first  time  —  that  is,  really  drawing  a 
conclusion  for  himself,  and  not  merely  repeating  words. 
He  would  begin,  we  may  say,  with  the  concept  '  iron.' 
But  if  this  concept  is  more  than  a  mere  word,  if  it 
really  means  anything,  it  must  have  been  formed  by  a 
number  of  judgments.  The  concept  'iron,'  if  it  has 
any  significance  for  the  person  using  it,  means  a  defi- 
nite way  of  judging  about  some  substance  —  that  it  is 
hard,  malleable,  tough,  etc.  The  greater  the  number 
of  judgments  which  the  concept  represents,  the  more 
meaning  or  significance  it  has;  apart  from  the  judg- 
ment, it  is  a  mere  word,  and  not   a  thought  at  all. 

To  admit,  then,  that  in  judging  we  always  start  from 
some  concept,  does  not  imply  that  there  is  a  different 
form  of  intellectual  activity  prior  to  judgment,  which 
furnishes  the  latter  with  ready-made  material  for  its 
use.  But,  as  we  have  seen,  in  ordinary  judgments  like 
the  example  with  which  we  have  been  dealing,  the  new 
judgment  is  a  further  expansion  or  development  of  a 
previous  set  of  judgments  which  are  represented  by  the 
concept.  The  concept,  then,  is  simply  the  series  of 
judgments  which  have  already  been  made.  Language 
comes  to  the  aid  of  thought,  and  makes  it  possible  to 
gather  up  such  a  set  of  judgments  and  represent  them 
by  a  single  expression  —  often  by  a  single  word.  Every 
word  that  is  the  name  of  some  logical  concept  repre- 
sents intellectual  work  —  the  activity  of  judgment  —  in 
its  formation.  In  learning  our  own  language,  we 
inherit  the  word  without  doing  the  work.  But  it  must 
never  be  forgotten  that  the  word   in  itself  is  not  the 


;i-:ss 

mentioned 
drawing  a 
ting  words. 
;ept   '  iron.* 
word,  if   it 
jrmed  by  a 
,'   if  it  has 
ians  a  defi- 
—  that  it  is 
;he  number 
s,  the  more 
n  the  judg- 
it  at  all. 
s  start  from 
\  a  different 
ment,  which 
crial  for  its 
orments  like 
ng,  the  new 
)pment  of  a 
mted  by  the 
le  series  of 
Language 
possible  to 
resent  them 
ord.     Every 
ncept  rcpre- 
:lgment  —  in 
nguage,    we 
But  it  must 
f  is  not  the 


§  74.     CONCLl'lS   AND   JUDGMENTS 


271 


concept.  To  make  the  thought  our  own,  to  gain  the 
real  concept,  it  is  necessary  to  draw  out  or  realize  to 
ourselves  the  actual  set  of  judgments  for  which  the 
word  is  but  the  shorthand  expression. 

The  view  which  regards  the  judgment  as  a  compound 
of  two  parts  —  subject  and  predicate  —  rests  upon  the 
substitution  of  words  for  thoughts.  It  analyzes  the 
proposition  (the  verbal  or  written  expression  of 
the  judgment),  instead  of  the  judgment  itself.  In 
the  proposition,  the  parts  do  exist  independently  of 
each  other.  The  subject  usually  stands  first,  and  is 
followed  by  the  predicate.  l>ut  there  is  no  such  order 
of  parts  in  a  judgment.  When  one  judges,  'it  is  rain- 
ing,' or,  'that  is  a  drum,'  the  piece  of  knowledge  is  one 
and  indivisible.  And  the  act  by  which  this  knowledge 
is  gained,  is  not  an  external  process  of  joining  one  part 
to  another,  but  is  an  intellectual  reaction  by  which  we 
recognize  that  something,  not  previously  understood, 
has  a  certain  meaning  or  significance. 

Again,  it  is  only  when  concepts  are  identified  with 
the  words  which  make  up  the  parts  of  the  proposition, 
that  they  can  be  regarded  as  ready-made  existences, 
which  are  quite  independent  of  their  connection  in  a 
judgment.  The  terms,  'iron,'  and  'metal,'  are  separable 
parts  of  the  proposition  and  exist  independently  of  their 
connection  with  it.  The  conclusion  has  been  therefore 
drawn  that  concepts  had  a  like  independence  of  judg- 
ments, but  might  enter  into  the  latter  and  form  a  part 
of  them  without  affecting  their  own  nature  in  any  way. 
But,  as  we  have  already  seen,  the  concept  has  no 
meaning  apart  from  the  series  of  judgments  which  it 


I   i 


I 


f 


I'  ■  ■  I  <  t 


It' 


I  (I 


.:i; 


272        JUDGMKNT   AS  Till",    IILEMKNIARV    I'RCXKSS 

represents.  And,  as  thinking  goes  on,  as  new  judg- 
ments are  made,  its  nature  is  constantly  changing.  In 
short,  concepts  are  not  dead  t/tinj^Sy  but  living  thoughts 
which  are  in  constant  process  of  develoi)ment. 

The  objection,  then,  which  urges  that  conception  is  a 
logical  process,  which  is  prior  to  judgment,  turns  out 
when  rightly  understood  to  be  no  objection  at  all.  For, 
in  the  light  of  what  has  been  already  said,  it  only 
amounts  to  this  :  In  making  new  judgments  regarding 
anything,  we  must  set  out  from  what  we  already  know 
of  it,  as  represented  by  the  judgments  already  made. 
That  is,  the  starting-point  for  a  new  judgment  is  the  con- 
cept or  series  of  judgments  which  represents  the  present 
state  of  our  knowledge.  The  progress  of  knowledge 
is  not  from  the  unknown  to  the  known,  but  from  a  state 
of  partial  and  incomplete  knowledge  to  one  of  greater 
perfection.  Thus  the  judgment  'gold  is  malleable' 
(supposing  it  to  be  a  real  judgment  made  for  the  first 
time),  adds  to,  or  develops  further,  our  existing  know- 
ledge of  gold,  as  represented  by  a  series  of  judgments 
previously  made  regarding  it. 

It  may  be  urged,  however,  that  not  every  judgment  can  grow  out 
of  previous  judgments  in  this  way.  For,  if  we  go  back  far  enough, 
we  must  reach  some  judgment  which  is  absolutely  first,  and  which 
presupposes  no  antecedent  judgment.  This  is  like  the  paradox 
regarding  the  origin  of  life.  If  all  judgments  are  derived  from  an- 
tecedent judgments,  how  was  it  possible  for  the  first  one  to  arise? 
It  will,  perhaps,  be  sufficient  answer  to  deny  the  existence  of  the 
paradox.  Consciousness  must  be  regarded  as  having  from  the  first 
the  form  of  a  judgment.  No  matter  how  far  one  goes  back  in  the 
history  of  consciousness,  one  will  always  find,  so  long  as  conscious- 
ness  is   present   at  all,    some  reaction,   however  feeble,   upon  the 


>i; 


iCKSS 


new  judg- 


:in<i-in<r, 


In 


ing  tJiougJits 

It. 

iception  is  a 
it,  turns  out 
at  all.    For, 
aid,  it   only 
ts  regarding 
Iready  know 
Iready  made, 
nt  is  the  con- 
s  the  present 
f   knowledge 
:  from  a  state 
le  of  greater 
s    malleable ' 
for  the  first 
isting  know- 
Df  judgments 


nt  can  grow  out 
back  far  enough, 
first,  and  which 
ke  the  paradox 
lerived  from  an- 
rst  one  to  arise? 
existence  of  the 
ng  from  the  first 
■roes  back  in  the 
n,<i;  as  conscious- 
eeble,   upon  the 


§  74.    CONCEPTS  AND   JUDGMKNTS 


273 


content,  and  sonicthinj^  like  knowlcd^^e  resuhin<i;.  Kven  the 
consciousness  ot  the  newly  born  infant,  reacts,  or  vaguely  judj^es, 
in  tiiis  way.  These  primitive  judgments  arc,  of  course,  very  weak 
and  confused,  but  they  serve  as  startini^-points  in  the  pnjcess  of 
intellectual  development.  (irowth  in  knowledge  is  simply  the 
process  by  means  of  which  these  vague  and  inarticulate  judgments 
are  developed  and  transformed  into  a  completer  and  more  coherent 
experience. 

References 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  pp.  9-16. 
F.  H.  Bradley,  T/ie  Principles  of  Loi^ic\  Bk.  I.  Ch.  I. 

B.  Bosanquet,  Logic,\<S[.  I.  Ch.  1.  §§  1-6. 

H.  Lotze,  Logic  (Eng.  trans.),  Vol.  I.,  ])p.  13-61. 

C.  Sigwart,  Logic,  §§  40-42. 

L.  T.  Hobhouse,  The  Theory  of  Kno%vledge,  Pt.  I.  Chs.  I.  and  11. 


rtifl 


s 

i'^ 


'\  1.1 


1  '■ 

> 

\ 

1 

1 

i^l 


i'l 


f'  II 


m 


m 


:i  ^' ' 


i 

,1' 
11  •(. 

Ill 


CHAPTER   XXI 

^  THE    MAIN    CHARACTERISTICS    OF    JUDGMENT 

§  75.  The  Universality  of  Judgments.  — We  have  now 
to  examine  the  nature  of  Judgment  a  little  more  closely 
than  we  have  clone  hitherto.  And,  in  the  first  place, 
we  note  that  all  judgments  claim  universality.  There 
are,  however,  several  kinds  of  universality,  and  more 
than  one  sense  in  which  a  judgment  may  be  said  to  be 
universal.  We  speak  of  a  universal  judgment  (more 
properly  of  a  universal  proposition),  when  the  subject  is 
a  general  term,  or  is  qualified  by  some  such  word  as 
'all,'  or  'the  whole.'  And  we  distinguish  from  it  the 
particular  judgment,  where  the  subject  is  only  the  part 
of  some  whole,  and  is  usually  preceded  by  'some,'  or  by 
other  partitive  words.  But  here  we  have  no  such  dis- 
tinction in  mind  ;  we  are  speaking  of  the  universality 
which  belongs  to  the  very  nature  of  Judgment  as  such, 
and  which  is  shared  in  by  judgments  of  every  kind. 

When  we  say  that  judgments  are  universal,  in  the 
sense  in  which  the  word  is  now  used,  we  mean  that  the 
conclusions  which  they  reach  claim  to  be  true  for  every 
one.  No  matter  what  the  subject  and  the  predicate 
may  be,  a  judgment,  e.^:,  'man  is  mortal,'  comes  forward 
as  a  fact  for  all  minds.  We  have  shown  in  the  last 
chapter  that  it  is  by  judging,  or  putting  things  together 
for  itself,  that  the  human  mind  gains  knowledge.    Now, 

274 


M' 


UliNT 

:  have  now 
iiorc  closely 

first  place, 
lity.     Tliere 
^  and  more 
)e  said  to  be 
;mcnt  (more 
ic  subject  is 
Lich  word  as 
from  it  the 
)nly  the  part 
some,'  or  by 
no  such  dis- 

univcrsality 
ent  as  such, 
^ry  kind, 
^ersal,  in  the 
lean  that  the 
rue  for  every 
the  predicate 
omes  forward 
n  in  the  last 
ings  together 
dedge.    Now, 


§75.     TlIK    UNIVKUSAI.II  V    ( >l     JL'lKiMKN  IS  2/5 

the  assumption  upon  whii'li  lliis  process  is  based  is 
that  the  result  thus  reached  —  kiiowleil^e  —  is  not  some- 
tMn<;  merely  individual  and  mcMnentary  in  character. 
Wiien  I  jiid.<;e  that  'two  and  two  are  f»)ur,'  or  that  'iron 
has  magnetic  i)r()perties,'  the  judgment  is  not  merely  a 
statement  of  what  is  going  on  in  my  individual  con- 
sciousness ;  but  it  claims  to  ex|)ress  something  which  is 
true  for  other  persons  as  well  as  for  me.  It  i)rofesses 
to  deal  with  facts  which  are  true,  and  in  a  seiise  inde- 
pendent of  any  individual  mind.  The  judgments  by 
which  such  conclusions  are  reached  are  universal,  then, 
in  the  sense  of  being  true  for  every  one  and  at  all  times. 
The  word  'objective'  has  essentially  the  same  meaning. 
Although  each  mai\  reaches  truth  only  by  actually  judg- 
ing for  himself,  yet  truth  is  objective,  out  there  beyond 
his  individual  or  '  subjective  '  thought,  shared  in  by  all 
rational  beings.  The  assum[)tion  uikju  which  .ill  argu- 
ment proceeds  is  that  there  is  such  a  standard,  and  that 
if  people  can  be  made  to  think  they  will  arrive  at  it. 
Thought  is  objective,  or,  in  other  words,  has  in  itself 
its  own  standard  of  truth. 

The  only  alternative  to  this  jMsition  is  scepticism,  or  pure  in- 
dividualism. If  Judgment  is  not  universal  in  the  sense  that  it 
reaches  propositions  wliich  are  true  for  everyhody,  it  is  of  course  im- 
possihle  to  find  any  standard  of  truth  at  all.  The  judgments  of  any 
individual  in  tliat  case  would  simply  have  reference  to  what  seems 
true  to  him  at  the  moment,  hut  could  not  be  taken  to  represent  any 
fixed,  or  permanent  tmth.  Indeed,  if  one  regards  Jud<;ment  as  deal- 
ing merely  with  particular  processes  in  an  individual  mind,  the 
ordinary  meanings  of  truth  and  falsehood  are  completely  lost,  and  it 
becomes  necessary  to  give  a  new  definition  of  the  words.  This  was 
the  position  of  the  Sophists  at  the  time  of  Socrates  (cf.  §  5).      Each 


'I 


i  '• 


iiifi 


li^f  I 


1 


276       THE   MAIN  CHARACTERISTICS  OF  JUDGMENT 

individual  man  was  declared  to  be  the  measure  of  what  is  true  and 
false,  as  well  as  of  what  is  good  and  bad.  There  is  thus  no  other 
standard  of  truth  or  value  tlian  the  momentary  judgment  (or  ca- 
price) of  the  individual.  Thih  is,  in  a  way,  the  rcditctio  ad 
absiirdiiin  of  scepticism. 

The  conmion  nature  of  truth,  as  .something  in  which  all  can 
share,  presupposes,  tlien,  a  common  mode  of  tliinking  or  judging  on 
the  part  of  all  rational  beings.  And  it  is  this  universal  type  or  form 
of  knowing  with  which  logic  deals.  The  question  as  to  whose 
thought  is  investigated,  or  in  what  individual  mind  the  thought  takes 
place,  is  in  itself  of  no  importance.  The  consciousness  of  a  savage 
diftcrs  very  greatly  from  that  of  an  educated  man ;  it  is  much  less 
complex  and  less  highly  developed.  But  yet,  in  spite  of  the  enor- 
mous differences,  there  exists  in  both  an  intelligence,  or  way  of 
thinking,  v.hich  shows  the  same  essential  character,  and  operates 
accordinji  to  the  same  fundamental  laws. 


:■?( 


V'lhs  \ 


Sf.' 


'^s'* 


hi: 


^5  ! 


*: 


§  'j^.  The  Necessity  of  Judgment.  —  The  secord  char- 
acteristic which  we  note  as  belonging  to  Judgment  is 
necessity.  By  this  we  mean  that  when  a  person  judges, 
he  is  not  free  to  reach  this  or  that  conclusion  at  will. 
As  an  intellectual  being,  he  feels  bound  to  judge  in  a 
certain  way.  This  is  sometimes  expressed  by  saying 
that  we  cannot  believe  what  we  choose,  v^e  must  believe 
what  we  can. 

In  many  of  the  ordinary  judgments  of  everyday  life, 
which  are  made  without  any  clear  consciousness  of  their 
grounds,  logical  necessity  is  implicitly  present  as  an  im- 
mediate feeling  of  certainty.  In  cases  of  this  kind,  we 
simply  identify  ourselves  with  the  judgment,  and  feci 
that  it  is  impossible  that  it  can  be  false.  But,  of  course, 
no  judgment  can  claim  to  be  necessary  in  its  own  right. 
Its  necessity  comes  from  its  connection  with  other  facts 


ENT 

t  is  true  and 
ms  no  other 
lent  (or  ca- 
rciiuctio  ad 

;iich  all  can 
r  judging  on 
type  or  form 
IS  to  whose 
hought  takes 
s  of  a  savage 
is  much  less 
of  tlie  enor- 
2,  or  way  of 
and  operates 


cord  char- 
idgment  is 
on  judges, 
on  at  will, 
judge  in  a 
by  saying 
ust  believe 


§  76.    THE  necp:ssity  of  judgment 


277 


eryday  life, 
ess  of  their 
it  as  an  im- 
lis  kind,  we 
t,  and  feel 
:,  of  course, 

own  right. 

other  facts 


which  are  known  to  be  true.  Or,  in  logical  terms, 
we  may  say  that  it  comes  from  reasons  or  premises 
which  support  it.  And  one  should  always  be  ready 
to  show  the  grounds  or  reasons  upon  which  one's 
feeling  of  necessity  rests.  But  in  ordinary  life,  as  we 
have  seen,  it  is  not  unusual  to  regard  a  conclusion  as 
necessary,  without  clearly  realizing  the  nature  of  the 
reasons  by  which  it  is  supported.  An  uneducated  man 
is  rarely  able  to  go  back  and  discover  the  reasons  for 
his  belief  in  any  statement  of  which  he  is  convinced. 
If  you  question  his  assertion,  he  feels  that  you  are 
reflecting  upon  ^ij  veracity,  and  consequently  grows 
angry.  In  the  feeling  of  immediate  necessity  or  con- 
viction, he  identifies  himself  with  the  judgment,  and 
does  not  see  that  the  criticism  is  not  directed  against 
the  latter,  but  against  the  grounds  by  which  it  is  sup- 
ported. 

In  this  distinction  between  necessity  that  is  merely 
felt,  and  the  necessity  that  is  conscious  of  its  own 
grounds,  we  see  the  direction  in  which  judgment  must 
develop.  In  the  evolution  of  thought,  we  must  become 
conscious  of  the  grounds  upon  which  our  judgments 
are  made.  That  is,  the  simple  judgment,  which  seems 
to  stand  in  isolation,  must  expand  so  as  to  unite  with 
itself  its  reasons.  By  itself,  it  is  only  a  f ragmen!:  of  a 
more  complete  and  widely  embracing  thought.  The 
feeling  of  necessity  is  an  evidence  of  its  dependence  and 
connection,  though  this  dependence  and  connection  upon 
other  facts  ma/  not  be  clearly  understood.  But  what 
is  implicit  m  "st  be  made  explicit ;  the  necessity  which 
is  merely /t'//  to  belong  to  the  simple  judgment  must 


i  i 


till 


I* 


.;  1^ 


4'M 


'■V 
ll,,. 


iHi. 


h 


H\ 


lii 
m 


!'it  ,!ii 


THE   MAIN   CHARACTERISTICS  OF  JUDGMENT 

be  justified,  by  showing  the  grounds  or  reasons  upon 
which  it  rests.  And,  for  this  purpose,  the  simple  judg- 
ment must  expand  so  as  to  include  the  reasons  which 
are  necessary  to  support  it.  In  other  words,  it  must 
develop  into  an  inference.  As  a  matter  of  fact,  the 
same  form  of  words  as  used  by  different  persons,  or  by 
the  same  person  at  different  times,  may  express  either 
a  judgment  or  an  inference.  Thus,  'the  price  of  wheat 
rose  after  the  war  began,'  might  express  either  a  simple 
historical  fact,  which  is  accepted  from  experience  or  from 
hearsay,  or  it  might,  in  the  mouth  of  a  person  acquainted 
with  the  laws  of  supply  and  demand,  be  the  necessary 
conclusion  of  a  number  of  premises.  Again,  a  child 
might  read  that,  'the  travellers  found  great  difficulty  in 
breathing  when  they  reached  the  top  of  the  mountain,' 
accepting  this  as  a  simple  statement  of  fact.  If  he  were 
to  read  this  same  statement  some  years  later,  however, 
he  would  probablv  connect  it  at  once  with  other  facts  re- 
garding the  nat  f  the  atmosphere,  and  the  action  of 
gravity,  and  so  pc    :civc  at  once  its  inferential  necessity. 

According  to  the  view  which  has  just  been  statv.d,  necessity  is  not 
a  property  which  belongs  to  any  judgment  in  itself,  but  something 
which  arises  through  its  dependence  upon  otlier  judgments.  In 
other  words,  necessity  is  ahvays  mediate,  not  immediate.  This 
view,  however,  differs  from  a  tlieory  tliat  was  once  generally  received, 
and  has  some  adherents,  even  at  the  present  time,  especially  among 
thinkers  who  belong  to  the  Scottish  or  'common-sense'  school.  In 
dealing  with  the  facts  of  experience,  we  always  explain  one  fact  by 
referring  it  to  a  second,  and  that  second  by  showing  its  dependence 
upon  some  third  fact,  and  so  on.  Thus  the  movement  of  the  piston- 
rod  in  an  engine  is  explained  by  the  pressure  of  steam,  and  this  is 
due  to  the  expansive  power  of  heat,  and  heat  is  caused  by  combus- 


I'rr 


ons  upon 
iple  judg- 
)ns  which 
5,  it  must 
;  fact,  the 
ons,  or  by 
ess  either 
;  of  wheat 
:r  a  simple 
ce  or  from 
icquainted 

necessary 
in,  a  child 
if^culty  in 
mountain,' 
If  he  were 
however, 

r  facts  re- 
e  action  of 

necessity. 

essity  is  not 

t  something 

nents.     In 

diate.     This 

ally  received, 

cially  among 

school.     In 

one  fact  by 

dependence 

)f  the  piston- 

1,  and  this  is 

I  by  combns- 


§  77.     JUDGMENT   BOTH    ANALYTIC   AND   SYNTMETIC     279 

tion  of  fuel,  etc.  We  are  thus  pushed  back  in  our  explanations  from 
one  fact  or  principle  to  another,  without  ever  reaching  anything 
that  does  not  require  in  its  turn  to  be  explained. 

Now,  it  is  said  that  this  process  cannot  go  on  forever ;  for  if  it 
did  there  could  be  no  final  or  complete  knowledge ;  the  whole 
system  would  be  left  hanging  in  the  air.  There  must,  therefore, 
it  is  argued,  be  some  ultimate  facts  which  furnish  the  support  for 
the  world  of  our  experience,  some  principle  or  principles  which  are 
themselves  necessary  and  do  not  require  any  proof.  That  is,  there 
must  be  certain  propositions  which  are  iinincdiatcly  necessary,  and 
which  serve  as  final  explanation  for  everything  else.  Now,  it  is 
clear  that  such  propositions  must  be  entirely  different  in  character 
from  the  ordinary  facts  of  experience,  since  their  necessity  belongs 
to  their  own  nature,  and  is  not  derived  from  any  other  source.  It 
had  to  be  supposed,  therefore,  that  they  stood  upon  a  different 
plane,  and  were  not  derived  from  experience.  To  explain  the  su- 
perior kind  of  certainty  which  they  were  assumed  to  possess,  it  was 
supposed  that  they  were  present  in  the  mind  at  birth,  or  were  innate. 
They  have  also  been  called  necessary  tnit/ts,  a  priori  truths,  and 
fundamental  first  principles^  in  order  to  emphasize  their  supposed 
distinction  from  facts  which  are  derived  from  experir    ;e. 

§  "ji.  Judgment  involves  both  Analysis  and  Synthesis.  — 

The  business  of  our  thought  is  to  understand  the  ways 
in  which  the  various  parts  of  the  real  world  are  related. 
And  a  judgment,  as  we  have  already  seen,  is  just  a 
single  act  of  thought,  —  one  step  in  the  process  of 
understanding  the  world.  Now  we  ask :  How  does 
Judgment  accomplish  its  task  .-*  Does  it  proceed  by 
analysis,  showing  the  parts  of  which  things  are  com- 
posed, or  does  it  employ  synthesis  in  order  to  show 
how  various  parts  combine  in  such  a  way  as  to  form 
a  whole .''  Or  is  it  possible  for  both  chese  processes  to 
be  united  in  one  and  the  same  act  of  judgment? 


1: 


\'>- 


if    I 


iJfj 


T' 


\ 


'  til 

^^B   '> 

1     |r  1 

•^I^Hil 

; 

Sjkl 

.Hi 

1' 

fl||! 

1 

'  ^^Hk  '' 

ij 

im'' 

• 

1    T? 

I 


I'" 


280       THE  MAIN  CIIARACrERISTICS  OF  JUDGMENT 

Suppose  that  one  actually  makes  the  judgment  for 
oneself  (and  does  not  merely  repeat  the  words),  '  the 
rose  has  pinnate  leaves.'  What  has  taken  place?  We 
notice,  firstly,  that  a  new  property  of  the  rose  has  been 
brought  to  light ;  a  distinction,  or  mark,  has  been  dis- 
covered in  the  content  *  rose,'  which  was  not  seen  to 
belong  to  it  before  the  judgment  was  made.  So  far, 
then,  the  process  is  one  of  analysis,  of  discovering  the 
parts  or  distinctions  of  something  which  is  at  first  taken, 
as  it  were,  in  a  lump.  And  this  is  a  most  essential  ele- 
ment in  all  thinking.  In  order  to  know,  it  is  absolutely 
necessary  that  the  differences  between  the  parts  of 
things  should  be  clearly  apprehended,  that  we  should 
not  confuse  things  which  are  unlike,  or  fail  to  make 
proper  distinctions.  If  we  examine  a  number  of  in- 
stances where  a  real  judgment  is  made,  we  shall  find 
that  this  moment  of  analysis,  or  discrimination,  is  always 
present.  Sometimes,  indeed,  analysis  may  not  seem  to 
be  the  main  purpose  of  the  judgment;  but  if  one  looks 
closely,  one  will  always  find  in  a  judgment  that  elements 
which  are  unlike  are  held  apart  or  discriminated. 

Let  us  look  again  at  the  same  judgment,  *the  rose 
has  pinnate  leaves.'  It  is  not  difficult  to  see  that  the 
discovery  of  something  new  in  itself  is  only  one  part  of 
what  the  judgment  has  accomplished.  The  judgment 
also  affirms  the  union  of  this  new  discovery  with  the 
properties  of  what  we  call  the  rose.  It  is,  therefore, 
from  this  point  of  view,  an  act  of  synthesis.  It  asserts 
that  the  prickly  branches,  fragrant  flowers,  feather-like 
leaves,  and  other  distinctions,  are  united  in  the  one 
content  which  we  call  the  rose.     It  does  not  stop  with 


I'j'iii; 


ENT 

gment  for 
ords),  'the 
ace  ?  We 
;  has  been 

been  dis- 
)t  seen  to 
.  So  far, 
vering  the 
irst  taken, 
iential  ele- 
absolutely 
i  parts  of 
we  should 
1  to  make 
ber  of  in- 

shall  find 
,  is  always 
3t  seem  to 

one  looks 
t  elements 
ted. 

'the  rose 
e  that  the 
ne  part  of 

judgment 
with  the 

therefore, 

It  asserts 
eather-like 
1  the  one 

stop  with 


§77.    JUDGMENT  BOTH   ANAIATIC  AND   SYNTHETIC    28 1 

the  mere  assertion,  *  there  is  a  mark  or  distinction,'  but 
it  affirms  that  it  is  a  mark  of  something,  i.e.,  that  it  is 
united  with  other  marks  or  properties  to  form  a  con- 
crete whole.  In  other  words,  we  may  say  that  every 
judgment  affirms  the  unity  of  the  different  parts,  or 
aspects,  of  a  thing ;  and  this  is,  of  course,  synthesis. 
From  this  point  of  view,  then,  Judgment  can  be  defined 
as  a  process  of  synthesis,  just  as  we  defined  it  above  as 
one  of  analysis. 

But  how,  it  may  be  asked,  is  it  possible  for  a  judg- 
ment to  be  both  analytic  and  synthetic  .'*  Are  not  these 
processes  directly  opposed  to  each  other .''  There  can 
be  no  doubt  that  this  is  the  case  when  we  are  dealins: 
with  material  things :  pulling  things  to  pieces  is  the 
opposite  of  putting  them  together.  When  we  are 
doing  the  one  we  cannot  also  be  doing  the  other.  But 
there  is  no  such  opposition  between  these  processes 
when  they  go  on  in  our  minds.  An  illustration  may 
make  this  clear.  Suppose  that  one  is  trying  to  under- 
stand some  piece  of  mechanism,  say  a  watch ;  in  order 
to  be  able  to  see  how  it  goes,  or  judge  correctly  regard- 
ing it,  two  things  are  necessary.  First,  one  must  notice 
all  the  parts  of  which  it  is  composed  —  the  wheels  of 
various  sizes,  springs,  pins,  etc.  But,  in  the  second 
place,  one  would  not  understand  the  watch  until  one 
saw  how  all  the  parts  were  united,  how  one  part  fits 
into  another,  and  all  combine  together  into  one  whole. 
We  do  not  mean  that  these  are  two  steps  which  take 
place  in  succession ;  as  a  matter  of  fact,  the  detection 
of  the  various  parts,  and  the  perception  of  their  connec- 
tion, go  hand  in  hand.     In  the  process  of  understanding 


(     '   ;' 


'♦ »      IH 


frf 


!  ■  I 


;:|:'^ 


:  i  I 


I« 


282       THE   MAIN   CHARACTERISTICS  01    JUDGMENT 


m 


!■ 


ii  .!'< 


th     i 


li.i 


I 


■ii 


f 


1  r 
?  f 


1:1  j 


P  <:: 


lla., 


i.ii 


the  watch,  we  have  looth  taken  it  to  pieces  and  put  it 
together  again  at  one  and  the  same  time.  Not  really, 
of  course,  but  in  our  thought.  In  the  world  of  material 
things,  as  we  have  said,  only  one  of  these  processes 
could  go  on  at  a  time ;  but  in  every  act  of  thinking, 
in  every  judgment,  analysis  and  synthesis  go  hand  in 
hand,  and  one  has  no  meaning  except  with  reference  to 
the  other. 

Although  every  judgment  contains,  as  we  have 
seen,  the  two  moments  of  analysis  and  synthesis,  these 
are  not  always  ei^aally  prominent.  The  main  purpose 
of  the  judgment  usually  falls  on  one  side  or  the  other. 
In  a  judgment  like,  *  water  can  be  divided  into  hydro- 
gen and  oxygen,'  the  main  emphasis  seems  to  be  on 
the  parts,  and  the  assertion  that  these  elements  are 
parts  of  a  ivholc,  though  present,  is  only  implied.  But 
when  one  asserts,  *  these  springs  and  wheels  together 
make  up  a  watch,'  it  is  the  nature  of  the  whole  upon 
which  the  emphasis  is  laid,  and  the  separation  or  dis- 
crimination of  the  parts,  is,  as  it  were,  secondary.  It  is 
not  difficult  to  see,  however,  that  the  two  moments  of 
Judgment  are  present  in  both  of  these  cases.  The  dif- 
ference consists  in  the  fact  that  at  one  time  analysis, 
and  at  the  other  synthesis,  is  made  the  main  purpose. 

It  was  at  one  time  supposed  that  analytic  and 
synthetic  judgments  were  entirely  different  in  kind 
from  each  other.  An  analytic  judgment,  it  was  said, 
is  one  in  which  the  predicate  is  obtained  by  analyzing, 
or  bringing  to  light,  what  is  contained  in  the  subject. 
Thus  the  judgment,  'all  material  bodies  fill  space,'  is 
analytic  ;  for  the  predicate  (space-filling)  is  contained  in 


III  tU- 


EXT 

ind  put  it 
s[ot  really, 
3f  material 
processes 
"  thinking, 

0  hand  in 
iference  to 

we    have 
lesis,  these 
in  purpose 
■  the  other, 
nto  hydro- 
5  to  be  on 
iments  are 
)lied.      But 
Is  together 
rholc.  upon 
ion  or  dis- 
lary.     It  is 
loments  of 
,     The  dif- 
le  analysis, 
purpose, 
lalytic    and 
It   in    kind 
:  was  said, 

analyzing, 
he  subject. 

1  space,'  is 
ontained  in 


§  77.     JUDGMENT   BOTH   AXAIATIC    AND    SYxNTllEIIC     283 

the  very  notion,  or  idea,  of  a  material  body.  All  that 
is  necessary  in  order  to  obtain  the  judgment  is  to  com- 
prehend the  meaning  of  the  subject.  An  analytic  judg- 
ment, then,  adds  nothing  to  our  knowledge.  Itjnerejy 
cnablcii,  US-  to  bring  to  light  and  express  what  is  con- 
tained in  tlia  idea,s  we  already  possess.  A  synthetic 
proposition,  on  the  contrary,  was  defined  as  one  in  which 
the  predicate  was  not  already  contained  in  the  subject, 
but  which  added  a  new  element  or  idea  to  it.  '  This  body 
weighs  ten  pounds,'  for  example,  is  a  .synthetic  propo- 
sition, for  one  cannot  obtain  the  predicate  by  analyzing 
the  subject.  The  predicate  adds  a  new  fact  which 
must  have  been  derived  from  experience. 

This  view  is  of  course  fundamentally  different  from  the  account 
of  Judgment  which  we  have  just  given.  The  absolute  disthiction 
between  analytic  and  synthetic  judgments,  like  the  theory  that 
thought  begins  with  concepts,  arises,  I  think,  from  a  substitu- 
tion of  the  spoken  or  written  proposition  for  the  judgment  itself. 
In  the  proposition  the  subject  seems  to  be  the  starting-point.  We 
have  a  word  or  term  which  appears  to  be  independent  and  capa- 
h\e  of  standing  alone.  The  question  is,  then,  where  shall  we  find 
the  predicate?  For  example  i'  he  proposition,  'iron  is  an  ele- 
ment,' the  subject  stands  first,  and  the  predicate  comes  later.  It 
seems  possible  then  to  say  that  we  have  first  the  subject  '  iron,'  and 
then  join  on  to  it  the  predicate  *  element,'  which  has  been  obtained 
either  by  analyzing  the  subject,  or  from  some  previous  experience. 
But  the  proposition,  as  a  collection  of  words,  must  not  be  substituted 
for  the  act  of  judgment.  Judgment,  as  we  have  already  seen,  is  a 
single  act  of  intelligence,  which  at  once  discriminates  and  brings 
into  relation  different  aspects  of  the  whole  with  which  it  is  dealing. 
A  mere  subject  by  itself  has  not  any  intelligible  meaning.  If  one 
hears  the  word  '  iron,'  for  example,  the  word  may  call  up  certain 
mental  images ;  but  l)y  itself  it  is  not  a  complete  thouglit  or  fact  in 


'ji 


I  1 


^ 


•f  • 


<<: 


MKiMtsas- 


l^\. 


I 


m 


t} 

'   ^'^n 

m 

■  f 

^^1' 

i^B' 

^^Bi 

S ' 

W. 

111 


u 


li'l 


,1  ^ 


284       THE    MAIN   CHARA(TKRISTI(S   f)F  JUDGMENT 

which  we  can  rest.  '  Well,  what  of  it? '  \vc  say.  The  mind  at  once 
goes  on  to  form  some  judgment  like,  'this  is  iron/  or  '  iron  is  heavy.' 
We  cannot  ////;//•  a  term  witliout  thinking  something  0/  it.  In  short, 
although  the  words  which  form  the  subject  of  a  proposition  are 
relatively  independent,  and  can  be  used  without  the  words  which 
make  up  the  predicate,  in  ?i  judgment^  on  the  other  hand,  a  subject 
is  only  a  .subject  ihfoiig/i  its  relation  to  a  predicate.  The  propo- 
sition may  be  divided  into  parts,  but  the  judgment  is  a  single 
thought-activity,  and  cannot  be  divided  (cf.  §  74). 

§  yS.  Judgment  as  Constructing  a  System  of  Knowledge. 

In  this  section  vvc  have  not  to  take  account  of  any  new 
characteristic  of  Judgment,  but  rather  to  emphasize 
the  part  it  plays  in  building  up  knowledge.  As  we 
have  seen,  Judgment  works  both  analytically  and  syn- 
thetically:  [it  discovers  new  parts  and  distinctions,  and 
at  the  same  time  brings  the  parts  into  relation  and  thus 
builds  up  a  whole^  That  is  the  law  according  to  which 
thinking  develops,  and  is  just  what  we  called  differen- 
tiation and  integration  in  a  previous  section  (§  72). 

It  is  necessary  here,  however,  to  dwell  upon  the  fact 
that  each  judgment  may  be  regarded  as  a  step  in  the 
process  of  building  up  a  system  of  knowledge.  The 
eraphatic  word  here  is  'system,'  and  we  must  be  per- 
fectly clear  about  its  meaning.  A  system  is  a  whole 
which  is  composed  of  various  parts.  But  it  is  not  the 
same  thing  as  an  aggregate  or  heap.  In  an  aggregate 
or  heap,  no  essential  relation  exists  between  the  units 
of  which  it  is  composed.  In  a  heap  of  grain,  or  pile  of 
stones,  one  may  take  away  any  part  without  the  other 
parts  being  at  all  affected  thereby.  '  But  in  a  system, 
each  part  has  a  fixed  and  necessary  relation  to  the  whole 


^ 

m 


0 


MENT 

mind  at  once 
iron  is  heavy.' 
*"  it.  In  short, 
yoposition  are 
I  words  which 
land,  a  subject 
The  propo- 
it   is  a   single 


Knowledge. 

of  any  new 
emphasize 
je.  As  we 
lly  and  syn- 
ictions,  and 
3n  and  thus 
ng  to  which 
ed  differen- 

(§  72). 
)on  the  fact 
step  in  the 
edge.  The 
lUst  be  per- 
is a  whole 
it  is  not  the 
n  aggregate 
2n  the  units 
n,  or  pile  of 
lit  the  other 
n  a  system, 
;o  the  whole 


§78.    CONSTRUCTING   A   SVSTKM   (W  KNOWMllXiK    285 

and  to  all  the  other  parts.  For  this  reason  we  may  say 
that  a  building,  or  a  piece  of  mechanism,  is  a  system. 
Each  stone  in  the  building,  each  wheel  in  the  watch, 
plays  a  part,  and  is  essential  to  the  whole.  In  things 
which  are  the  result  of  growth,  the  essential  relations  in 
which  the  parts  stand  is  even  more  clearly  evident. 
The  various  parts  of  a  plant  or  an  animal  have  each  their 
own  function,  but  at  the  same  time  they  are  so  neces- 
sary to  each  other  that  an  injury  to  one  is  an  injury  to 
all.  We  express  this  relation  in  the  case  of  living  things 
by  saying  that  the  parts  ire  organic  to  each  other.  And, 
in  the  same  way,  it  is  not  unusual  to  speak  of  society  as 
an  organism,  in  order  to  express  the  fact  that  the  vari- 
ous individuals  of  which  it  is  composed  are  not  inde- 
pendent units,  but  stand  in  necessary  relations  to  one 
another,  and  are  all  mutually  helpful  or  hurtful. 

We  have  said  that  Judgment  constructs  a  system  of 
knowledge.  This  implies,  then,  that  it  is  not  merely 
a  process  of  adding  one  fact  to  another,  as  we  might 
add  one  stone  to  another  to  form  a  heap.  No  !  Judg- 
ment combines  the  new  facts  with  which  it  deals,  with 
what  is  already  known,  in  such  a  way  as  to  give  to 
each  its  own  proper  place.  Different  facts  are  not 
only  brought  together,  but  they  are  arranged,  related, 
systematized.  No  fact  is  allowed  to  stand  by  itself,  but 
has  to  take  its  place  as  a  member  of  a  larger  system 
of  facts,  and  receive  its  value  from  this  connection.  Of 
course,  a  single  judgment  is  not  sufficient  to  bring  a 
large  number  of  facts  into  relation  in  this  way.  But  each 
judgment  contributes  somctJiing  Xo  this  end,  and  brings 
some  new  fact  into  relation  to  what  is  already  known. 


v\\\\ 


i 


m 


'•^  'k 


■  * 


T' 


1 


» 


'Wj  ML 
MM 

1 

T 
1 

1 
11^ 

1 1^ 


HI 


'<  ( 


'I 


^^'^^libfj- 


ivi 


It 

!li   .aii 


286        rilE   MAIN  CIIARACrERISTICS  Ol-'  JUDGMENT 

In  a  simple  judgment  like,  'that  was  the  twelve  o'clock 
whistle,'  the  constructive  or  systematizing  work  accom- 
plished is  evident.  The  auditory  sensation,  which  in 
itself,  as  a  mere  wandering  sound,  was  not  a  piece  of 
knowledge  at  all,  is  interpreted  in  such  a  way  as  to  find 
a  place  in  the  system  of  experience.  One  may  appreciate 
what  part  the  judgment  really  plays  by  remembering  how 
the  sound  appeared  before  one  was  able  to  judge.  There 
may  have  been  at  first  a  moment  of  bewilderment — 
'  What  does  this  mean  ? '  one  asks.  In  the  next  moment 
the  judgment  is  made :  '  It  is  the  twelve  o'clock  whistle.' 
That  is,  our  thinking  has  constructed  a  meaning  for  it, 
and  brought  it  into  relation  with  the  rest  of  our  know- 
ledge. 

(i)  Every  new  experience  is  thus  Ijrought  into  relation  with  the 
facts  wliicli  we  already  know,  and  is  tested  by  them.  It  has  to  find  its 
place  in  the  system  of  knowledge  —  to  join  itself  to  what  is  already 
known.  If  this  is  impossible,  if  what  claims  to  be  a  fact  is  entirely 
opposed  to  what  we  already  know  on  the  same  subject,  it  is  usually 
declared  to  be  false.  Thus,  we  would  refuse  to  believe  that  some 
person  whom  we  know  well  and  respect  was  guilty  of  theft ;  for  it 
would  be  impossible  to  connect  such  conduct  with  what  we  already 
know  of  his  character.  And,  similarly,  we  find  it  impossible  to 
believe,  even  although  we  have  the  evidence  of  our  senses,  that  the 
conjurer  lias  actually  performed  what  he  professes ;  for  to  do  so 
would  olten  be  to  reverse  entirely  our  conception  of  natural  laws.  It 
must  not  be  forgotten,  however,  that  the  existing  system  of  know- 
ledge, which  seems  to  serve  as  the  standard  and  test  of  new  facts,  is 
itself  undergoing  constant  modification  through  the  influence  of 
these  facts.  As  new  experiences  are  brought  into  connection  with 
the  existing  body  of  our  knowledge,  there  is  a  constant  rearrange- 
ment and  readjustment  of  the  latter  going  on.  Usually  this  adjust- 
ment is  slight,  and  takes  place  almost  imperceptibly.     But,  in  some 


MKNT 

L'lvc  o'clock 
vork  accom- 
ti,  which  in 
a  piece  of 
ly  as  to  find 
y'  appreciate 
iberinij^  how 
Ige.  There 
ilderment — 
.\xt  moment 
)ck  whistle.' 
nini;  for  it, 
;  our  know- 


ation  with  the 
has  to  find  its 
hat  is  aheady 
act  is  entirely 
t,  it  is  usually 
ve  that  some 
■  theft ;  for  it 
lat  we  already 
impossible  to 
uses,  that  the 
for  to  do  so 
:ural  laws.  It 
tern  of  know- 
if  new  facts,  is 
;  influence  of 
nnection  with 
ant  rearrange- 
ly  this  adjust- 
But,  in  some 


§  78.    CONSTRUCTING   .\   SYSTEM   OF   KN'OWLEUOIO     287 

cases,  a  single  fact  may  be  so  significant  as  c()ni[)letely  to  transform 
what  seemed  to  be  the  accumulated  knowledge  of  years.  The 
experiment  which  (lalileo  m.ule  i)y  dropping  halls  of  difterent 
weight  from  the  tower  of  Pisa,  made  it  impossible  to  hold  any  longer 
the  old  theory —  which  seemed  as  certain  as  anything  well  could  be 
—  that  the  velocity  with  which  bodies  fall  is  proportional  to  their 
weight.  Again,  if  theft  were  actually  proved  against  the  man  we 
respect,  that  single  fact  might  be  sufficient  to  force  us  io  give  up 
everything  which  we  supposed  that  we  knew  about  his  character. 

(2)  We  have  said  that  judgment  is  the  process  by  which  know- 
ledge grows  into  a  system.  It  is  by  judging  or  thinking  that  we 
attempt  to  bring  the  various  parts  of  our  experience  into  relation 
with  one  another.  The  degree  to  which  this  has  been  done  is  the 
measure  of  our  intellectual  development.  The  knowledge  of  tin; 
uneducated  and  unthinking  man,  like  that  of  the  child,  is  largely 
composed  of  unrelated  fragments.  It  is  an  aggregation,  not  a 
system  of  facts.  The  facts  which  go  to  make  it  up  may  quite  well 
be  contradictory,  but  this  contradiction  is  not  seen  because  no 
attempt  is  made  to  unite  them.  There  is,  of  course,  no  human 
experience  which  is  entirely  systematic,  or  which  has  been  com- 
pletely unified.  Even  those  who  have  thought  most  deeply  find  it 
impossible  to  fit  together  exactly  knowledge  gained  from  ditiferent 
fields,  and  from  difTerent  sciences.  The  facts  of  one  science,  for 
example,  may  seem  to  stand  by  themselves,  and  not  to  have  any 
relation  to  the  facts  derived  from  another  science.  Or  there  may 
appear  to  be  a  conflict  between  the  results  of  physical  sciences, 
and  the  truths  of  moral  philosophy  and  religion.  But  the  ideal 
always  remains  that  truth  is  one  and  indivisible,  and  that  it  must 
be  possible  ultimately  to  harmonize  all  facts  in  one  all-embracing 
system  of  judgment. 

References 

B.  Bosanquet,  T/k;  Essoitiah  of  Logic,  Lecture  II. 
"  "  Logic,  Vol.  I.,  pp.  97-103. 

C.  Sigwart,  Logic,  §  18. 


I,     1 


r 


..  t 


I 


i] 


CHAPTER   XXII 


THE    LAWS   OF   THOUGHT 


<  H 


:           il=i 

1           ' 

liii , 

:      15 
Pi 

i       i 

lid 

§  79.  The  Law  of  Identity.  —  Wc  found  (§  73)  that 
Judgment  is  the  simplest  form  of  tiiinking.  And,  in 
the  last  chapter,  wc  were  engaged  in  studying  its  main 
characteristics,  and  becoming  acquainted  with  its  mode 
of  operation.  The  essential  nature  of  the  thinking 
process,  therefore,  has  already  been  stated,  though  we 
have  not  traced  the  mode  of  its  development,  nor  shown 
its  application  to  the  various  problems  of  experience.  In 
nearly  all  books  dealing  with  logic,  however,  one  finds  a 
statement  of  three  fundamental  laws  of  thought  which 
differ  greatly,  in  form  at  least,  from  what  we  have  so 
far  learned  regarding  the  nature  of  Judgment.  These 
laws  are  so  well  known  by  name,  and  yet  so  ambiguous 
in  their  mode  of  statement,  that  it  seems  well  to  try  to 
decide  what  meaning  to  apply  to  them.  It  will  also  be 
interesting  to  note  their  relation  to  the  discussion  of 
Judgment  already  given.  They  are  usually  regarded  as 
axioms,  or  propositions  which  require  no  proof,  rather 
than  as  descriptive  of  the  nature  of  thought.  In  this 
sense,  they  are  supposed  to  be  the  foundation  of  all 
logic,  since  they  are  presupposed  in  all  thinking. 

The  first  of  these  laws,  or  axiomatic  principles,  is  that 
of  Identity.  Whatever  is,  is  ;  everything  remains  iden- 
tical with  itself ;  A  is  A.  These  are  some  of  the  forms 
in  which  the  law  is  usually  stated.     In  all  argument,  we 

288 


»  w 


(§  73)  that 
g.  And,  in 
\ng  its  main 
ith  its  mode 
he  thinkinrr 
,  thouj^h  we 
t,  nor  shown 
)eriencc.  In 
',  one  finds  a 
3u<;l"it  which 
we  have  so 
ent.  These 
0  ambiguous 
/ell  to  try  to 
will  also  be 
liscussion  of 
regarded  as 
Droof,  rather 
ht.  In  this 
lation  of  all 
iking, 

iples,  is  that 
cmains  iden- 
of  the  forms 
rgumcnt,  we 


§  yy.      TilH    I, AW   ()!•    IDKNllTV 


289 


assume  at  least  that  each  thing  possesses  a  permanent 
character,  and  does  not  i)ass  now  into  this,  now  into 
that.  If  any  knowledge  is  to  l)e  possible  at  all,  the 
character  of  things  must  remain  fixed.  Socrates  is 
always  to  be  Socrates,  and  iron,  iron.  Mvery  one  as- 
sumes as  much  as  this,  though  he  may  not  himself  be 
conscious  of  it  (cf.  §  9). 

Another  inter[)retation  of  this  [)rinciple  was,  how- 
ever, offered  by  lioole  and  Jevons,  who  developed  what 
is  known  as  the  ICquational,  or  Symbolic  logic.  Accord- 
ing to  these  writers,  tlie  law  of  Identity  e.xjn-esses 
the  fundamental  nature  of  Judgment.  That  is  to  say, 
every  judgment  is  the  expression  of  an  identity  between 
the  subject  and  the  predicatej  Tlie  jutlgment,  'New 
York  is  the  largest  city  in  America,'  is  simply  a  case  of 
a  is  a.  It  expresses  the  fact,  that  is,  that  New  York 
and  the  largest  city  in  America  are  identical.  '  Iron  is 
a  metal,'  is  another  example  of  the  same  principle.  It 
may  be  written :  iron  =  metal.  And,  since  the  copula 
may  often  be  ambiguous,  it  will  be  better  to  discard  it 
in  working  out  arguments,  and  adopt,  in  its  place,  the 
sign  of  equality. 

Judgment,  then,  is  simply  an  equation,  and  may  be 
written  as  such.  Further,  the  conclusion  of  a  series  of 
logical  premises  may  be  obtained  by  a  process  similar 
to  that  employed  in  working  algebraical  equations. 
That  is,  we  can  substitute  for  any  term  in  a  judgment, 
its  equivalent,  or  the  value  which  it  has  in  another 
judgment.  This  method  Jevons  calls  'the  substitution 
of  similars,'  which  he  maintains  is  the  fundamental 
principle  of  all  reasoning. 


u 


W 


4iii 


I. 


r' 


0 


H 


> 


^ 


m 


j<  H 

.j 

• 

■    . 

l» 

'ii 

■     'i      ; 

i    [ 

i 

*"  1 

'  1 

I 
1  ( 

H 

■1 


290  THE  LAWS  OF  THOUGH  r 

It,  now,  wc  employ  letters  to  symbolize  the  terms  of 

the   propositions,  it   is   claimed   that  we  can  work  out 

any  argument   by   the   equational  method.     Take  the 

argument, 

All  metals  are  elements, 

Iron  is  a  metal, 

Therefore  iron  is  an  element. 

Now  represent  metal  by  M  ;  iron  by  I ;  and  element  by 
E.     Then  the  argument  in  equational  form  will  be, 

M  =  E (i) 

I  =  M (2) 

and  by  the  substitution  in  (i)  of  the  value  of  M  in  (2) 
we  get  I  =  E,  the  required  conclusion. 

Or,  we  may  illustrate  this  method  by  a  somewhat 
more  complex  example  which  is  also  taken  from  Jevons  : 
*  Common  salt  is  sodium  chloride,  which  is  a  substance 
that  crystallizes  in  cubical  form  ;  but  what  crystallizes 
in  cubical  form  does  not  possess  the  power  of  double 
refraction.'  The  conclusion  of  this  argument  may  be 
found  by  letting  A  =  Common  Salt,  B  =  Sodium  Chlo- 
ride, C  =  something  which  crystallizes  in  cubical  form, 
and  D  =  something  which  possesses  the  power  of  double 
refraction.  The  negative  of  any  of  these  terms  will  be 
expressed  by  the  corresponding  small  letters.  The  argu- 
ment may  now  be  expressed  :  — 

A  =  B (.) 

B  =  C (2) 

C  =  d (3) 

By  substitution  of  the  value  of  C  in  (2)  we  get, 

B  =  d (4) 

And  substituting  here  the  value  of  B  in  (1), 

A  =  d 


he  terms  of 

n  work  out 

Take  the 


^'  \  m 


element  by 
will  be, 

.    .    .    (0 

...       (2) 

;  of  M  in  (2) 

a  somewhat 
Erom  Jevons : 
;  a  substance 
t  crystallizes 
er  of  double 
ent  may  be 
odium  Chlo- 
ubical  form, 
ver  of  double 
erms  will  be 
The  argu- 


(0 

(2) 

(3) 
(4) 


get, 


§  79.     THE   LAW   OF   IDENTITY 


291 


Giving  to  these  symbols  their  meanings,  we  get  the 
result  *  common  salt  does  not  possess  the  power  of 
double  refraction,'  which  is  the  conclusion  of  the  argu- 
ment. 

Of  course,  in  simple  arguments  like  those  we  have 
been  examining,  there  is  nothing  gained  by  the  use 
of  symbols,  and  the  representation  of  arguments  in 
this  form.  But  when  the  various  terms  employed  are 
much  longer  and  more  complex,  simpUfi cation  may  be 
attained  in  this  way.  Various  other  symbols  have  also 
been  used  to  express  the  relation  of  the  various  terms 
to  each  other,  and  a  symbolic  logic  has  been  developed 
which  follows  very  closely  the  procedure  of  algebra. 
The  examples  given  may,  however,  serve  as  illustrations 
of  this  method.  ^ 

It  is,  however,  as  a  tJieory  of  the  meaning  of  Judg- 
ment that  we  are  interested  in  this  mode  of  interpreting 
the  law  of  Identity,  We  have  seen  that  it  works  fairly 
well  in  practice,  and  therefore  cannot  be  wholly  false. 
But  there  are  certain  forms  of  reasoning  in  which  it  will 
not  work.  We  cannot  get  the  conclusion  by  the  equa- 
tional  method  in  an  example  like  the  following :  *  B  is 
greater  than  A,  C  is  greater  than  B,  therefore  C  is  still 
greater  than  A.' 

This  practical  objection  being  left  out  of  account,  we 
have  to  ask  whether  an  equation  represents  fairly  the 
nature  of  Judgment.     Does  a  judgment  express  merely 

^  The  clearest  statement  of  the  aims  and  methods  of  the  Equational 
Logic  ma}'  perhaps  be  obtained  from  Jevons,  TJie  Principles  of  Scirncr, 
Introduction.  Cf.  also  G.  Boole,  An  Investigation  0/  the  Laws  of  Thought. 
London,  1854. 


<  m 


!|J  . 


I;  "* 


;:'  !i< 


1  ; 


'i  i' 


.1, 


w 


muk 


JMaMWUiB 


HMMMMMiaiH 


292 


THE  LAWS   OF  THOUGHT 


]\ 


f    ffia' 

wmh 

1 

5'i' 

^^H 

^M  1 

''HHh'  : ' 

I 


11  ;  ..  I  . 


W 


0ti 

I 


il 


* 


the  identity  of  subject  and  predicate  ?  And  if  so,  what 
kind  of  identity  is  referred  to  ?  In  matlicmatical  rea- 
soning, the  sign  of  cquaHty  expresses  the  identity  of 
quantitative  units.  When  one  says,  2  +  3  =  5,  the 
meaning  is  that  the  number  of  units  on  each  side  of 
the  equation  is  identical.  And,  similarly,  the  assertion 
that  a  parallelogram  =  2  triangles  with  the  same  base 
and  of  the  same  altitude  as  itself,  expresses  the  fact  that, 
in  the  two  cases,  the  number  of  units  of  area,  square 
feet,  square  yards,  etc.  is  the  same.  In  mathematics,  the 
equation  declares  that  the  quantitative  relations  of  its 
two  sides  are  identical.  It  does  not  assert  that  the  two 
things  compared  —  the  triangle  and  one  half  the  par- 
allelogram, for  example  —  have  the  same  qualities,  or 
are  exactly  the  same  in  all  respects.  Now,  if  we  ex- 
tend the  use  of  the  sign  of  equality,  it  must  take  on 
a  new  meaning.  It  is  clear  that  in  a  judgment  like 
'iron  =  metal,'  there  is  no  reference  at  all  to  quantita- 
tive relations.  We  are  not  asserting  that  the  number 
of  units  in  the  two  terms  is  identical.  What,  then,  does 
the  sign  of  equality  express  in  such  a  case.-* 

The  answer  is  not  difficult,  say  those  who  hold  this 
theory.  The  sign  of  equality  in  such  cases  expresses 
absolute  identity ;  the  entire  and  complete  sameness  of 
subject  and  predicate.  The  proposition,  'mammals  = 
vertebrates,'  asserts  that  mammals  and  vertebrates  are 
one  and  the  same  thing.  But  that  statement  in  its 
present  form  is  not  true :  the  class  mammal  does  not 
completely  correspond  with  the  class  vertebrate.  To 
make  it  exact,  say  those  who  uphold  the  equational 
form,  one  must  qualify  or  liniit  the  predicate  and  write 


1  if  so,  what 
smatical  rea- 
:  identity  of 

f-  3  =  5.   the 
sach  side  of 
he  assertion 
J   same  base 
:hc  fact  that, 
area,  square 
icmatics,  the 
ations  of  its 
that  the  two 
alf   the   par- 
qualities,  or 
w,  if  we  ex- 
fiust  take  on 
dgment   like 
to  quantita- 
the  number 
at,  then,  does 

ho  hold  this 
ies  expresses 
sameness  of 
mammals  = 
rtebrates  are 
ement  in  its 
iial  does  not 
tebrate.  To 
le  equational 
ite  and  write 


§  79.    THE   LAW  OF  IDENTITY 


293 


the  proposition,  '  mammals  =  some  vertebrates.'  But, 
even  so,  we  may  urge,  the  form  of  the  judgment  is  still 
defective.  In  the  first  place,  it  does  not  correspond  to 
the  model  a  =  a.  For  one  side,  *  mammal,'  is  clearly 
marked  off,  while  the  other  is  indefinite  and  vague. 
And,  secondly,  just  because  of  its  vagueness,  it  is  not 
a  satisfactory  piece  of  knowledge.  To  obviate  these 
objections,  one  must  go  further  and  write,  mammals  = 
mammalian  vertebrates.  At  last  the  judgment  seems 
to  correspond  to  the  type,  a  =  a.  But  a  new  difficulty 
arises.  Has  not  the  judgment  lost  all  its  original  mean- 
ing and  become  a  mere  tautology }  There  seems  to  be 
no  escape  from  the  following  dilemma :  cither  there  is 
some  difference  between  subject  and  predicate,  and  the 
judgment  is  therefore  not  in  the  form  a  —  a,  or  the  judg- 
ment is  tautologous  a  id  expresses  nothing.  The  view 
of  the  equational  logic  that  Judgment  affirms  the  entire 
identity  of  subject  and  predicate  refutes  itself.  The 
form  a  =  a  cannot  be  regarded  as  the  type  to  which  all 
judgments  conform. 

But  there  must  be  some  kind  of  identity  between  the 
parts  of  a  judgment.  In  one  sense,  we  do  seem  to 
declare  that  the  subject  and  predicate  are  identical 
when  we  say,  'iron  is  a  metal'  As  we  have  seen,  how- 
ever, if  these  terms  are  merely  identical  and  nothing 
more,  the  judgment  loses  all  meaning.  We  are  forced 
to  the  conclusion  that  every  judgment  affirms  both 
identity  and  difference,  or  that  there  is  identity  running 
through  and  underlying  the  diversity.  But  is  not  this 
a  paradoxical  statement  .<*  When  we  affirm  identity, 
does  not  this  imply  the  absence  of  all  difference  .-*     If 


*0M 

I      I 


m 


ij  -  -.» 


I    ! 


^1 


./, 


^i-asaas^ 


i\ 


i 

it 


m 

l>''it'' 

m 


ini;' 


MMW 


* 


ul!ii;l 


mmam 


wm 


294 


THE   LAWS   OF  THOUGHT 


a  is  a,  how  can  it  at  the  same  time  be  something  differ- 
ent from  itself  ? 

And  yet  this  is  just  what  every  judgment  which  has 
any  meaning  affirms.  'Iron  is  fusible.'  'This  table  is 
made  of  oak.'  'The  sword  is  rusty  with  age.'  In  all 
these  judgments  there  is  an  assertion  of  the  unity  of 
different  properties  or  parts  in  one  whole.  A  is  B,  and 
yet  does  not  cease  to  be  A,  is  rather  the  type  of  judg- 
ment than  a  is  merely  or  abstractly  a.  It  is  worth 
noticing  that  this  view  of  the  matter  corresponds  with 
the  account  of  Judgment  already  given.  We  saw 
that  Judgment  constructs  a  system  of  knowledge  by 
showing  that  various  things,  which  seem  at  first  unre- 
lated, are  yet  connected  by  an  underlying  unity.  Know- 
ledge is  always  the  synthesis  or  union  of  different  parts 
or  different  properties  in  a  comnici  identity.  And 
each  judgment,  as  an  element  of  knowledge,  displays 
the  same  essential  structure  which  belongs  to  knowledge 
as  a  whole.  It  involves,  as  was  shown  in  (§  'j'j\  both 
analysis  and  synthesis,  and  declares  the  oneness  or 
identity  of  a  number  of  properties  or  parts,  without  at 
the  same  time  losing  sight  of  their  distinctness. 

Let  us  now  sum  up  our  discussion  of  the  law  of  Iden- 
tity. When  rightly  understood,  as  we  have  seen,  it  does 
not  affirm  that  a  can  only  be  bare  a,  that  the  subject 
and  predicate  are  absolutely  identical.  It  Is  a  law  of 
thought,  and  expresses  the  fact  that  Judgment  brings 
together  differences  ;  i.e.,  different  things  and  qualities, 
and  shows  that  they  are  parts  of  one  whole  or  unity. 
It  reveals  the  underlying  unity  or  identity  which  is 
present  in  the  midst  of  variety.     This  law  also  states 


§  8o.     THE   LAW   OF   CONTRADICTIOX 


295 


ithing  differ- 

it  which  has 
This  table  is 
ige.'  In  all 
the  unity  of 
A  is  B,  and 
ype  of  judg- 
It  is  worth 
;sponds  with 
1.  We  saw 
lowledge  by 
it  first  unre- 
nity.  Know- 
fferent  parts 
itity.  And 
ge,  displays 
o  knowledge 
(§  n\  both 
oneness  or 
s,  without  at 
iess. 

law  of  Iden- 
seen,  it  does 
the  subject 
Is  a  law  of 
ment  brings 
nd  qualities, 
)le  or  unity. 
ty  which  is 
V  also  states 


another  characteristic  of  Judgment  which  we  have 
already  emphasized.  This  is  what  we  have  called  the 
universality  of  Judgment  (§  75).  It  is  to  judgments,  and 
not  to  concepts  or  terms,  as  has  sometimes  been  sup- 
posed, that  the  law  of  Identity  properly  applies.  What 
it  affirms  in  this  connection  is  simply  that  Judgment 
claims  to  be  true,  and  hence  is  identical  at  all  times 
and  for  all  persons.  It  cannot  be  true  for  you  and 
false  for  me  that,  'iron  is  a  metal.'  Truth  is  not  a 
matter  of  individual  taste,  but  every  judgment  which 
is  true  has  a  permanent  character  or  identity  belonging 
to  it. 

§  80.  The  Law  of  Contradiction.  —  The  law  of  Contra- 
diction is  the  second  of  the  so-called  laws  of  thought. 
It  is  usually  stated  as  follows :  It  is  impossible  for  the 
same  thing  both  to  be  a^  and  not  to  be  rt- ;  or,  a  is  not 
not-a.  It  is  evident  that  this  law  states  in  a  negative 
form  the  same  characteristics  of  thought  as  the  law  of 
identity.  Indeed,  it  was  in  this  form  that  the  principle 
was  first  laid  down  by  Aristotle.  "  It  is  impossible," 
he  says,  "that  the  same  predicate  can  both  belong  and 
not  belong  to  the  same  subject  at  the  same  time,  and 
in  the  same  sense."  ^  We  cannot  assert  in  the  same 
sense  that  Socrates  is  both  wise,  and  not  wise.  Truth 
is  not,  as  the  Sophists  supposed,  a  matte»*  of  taste  or 
convenience,  but  must  be  consistent  with  itself.  If  a 
judgment  affirms  that  'iron  is  a  metal,'  it  at  the  same 

^  Metaphysics,  Bk.  III.  Ch.  IV.  See  also  the  remaining  chapters  of 
the  same  boolc  for  Aristotle's  demonstration  that  all  thought  presupposes 
such  a  principle. 


I!  Ij 
J 


., .  «.«^».««B»  -fCK  CT«^«..«- 


I 


ij 


'ii  . 


•  i 

lli 

i"  [ 

1- 

i 

ilk, 

1 

i!i 


B 

• 

^1», 


:  1 1 


296 


THE   LAWS  OF  THOUGHT 


time  excludes  the  assertion  that  it  is  not  a  metal. 
There  is  a  fixity  and  permanence  about  judgments 
which  prevents  them  from  changing  into  anything  else. 
And  it  is  just  this  permanence  which  we  have  already 
called  the  universality  of  Judgment,  which  the  law  of 
Contradiction  expresses  in  a  negative  form. 

The  law  of  Contradiction  has,  however,  sometimes 
been  interpreted  in  such  a  way  as  to  make  it  equivalent 
to  the  assertion  of  abstract  or  bare  identity  which  we 
found  in  the  Equational  logic.  That  is,  the  statement 
that  it  is  impossible  for  any  judgment  to  unite  a  and 
not-a  may  be  taken  to  mean  that  it  is  impossible  to 
assert  the  unity  of  a  and  anything  different  from  a. 
But,  as  we  have  seen,  this  is  exactly  what  we  do  in 
every  judgment  which  is  more  than  a  tautology.  The 
law,  then,  does  not  forbid  the  union  of  differences  in 
one  judgment,  but  of  contradictories,  or  of  what  would 
destroy  the  integrity  of  the  judgment  and  render  it 
unmeaning.  If  the  law  is  to  hold  true  of  Judgment, 
not-a  must  not  be  taken  as  equivalent  to  anything  which 
is  different  from  a,  but  as  signifying  what  is  opposed,  or 
contradictory  to  a. 

It  is  not  by  any  means  easy  to  decide  what  things  are  merely 
different,  and  therefore  compatible  with  each  other,  and  what  con- 
tradictory or  opposed.  Logic  can  give  no  rule  which  may  be  applied 
in  every  case.  If  experience  shows  that  two  things,  or  two  proper- 
ties, are  at  any  time  united,  we  say  that  they  are  merely  different 
from  each  otJier ;  if  they  have  never  been  found  in  conjunction  and 
we  are  not  able  to  conceive  how  their  union  could  take  place,  we 
call  them  opposites  or  contradictories.  It  is  worth  noticing,  too. 
that  no  terms  are  ///  thcnisctvcs  contradictory,  except  those  which 
are  in  the  form  a  and  not-a,  wise  and  not-wise.     But  they  become 


§Si.    THE   LAW  OF   r.XCLU[)KI)    MIDDT^E 


t   a   metal. 

judgments 
^tiling  else. 
:ive  already 

the  law  of 

sometimes 
:  equivalent 
y  which  we 
;  statement 
inite  a  and 
ipossible  to 
cut  from  a. 
it  we  do  in 
)logy.  The 
iffcrenccs  in 
what  would 
d  render  it 

Judgment, 
thing  which 

opposed,  or 

2:s  are  merelv 
and  what  con- 
iiay  be  applied 
or  two  proper- 
crely  different 
)njunction  and 
take  place,  we 
noticing,  too. 
)t  those  whidi 
ut  they  becoifu 


-97 


contradictory  and  exclude  each  other  when  tlicy  claim  to  occupy 
the  same  phice  in  some  particular  system  of  facts.  Thus  '  maple  ^ 
and  'oak''  denote  trees  of  a  different  variety,  which  are,  however,  so 
little  opposed  that  they  may  exist  side  by  side.  If  both  these  terms 
were  applied  to  the  same  tree,  however,  they  would  become  con- 
tradictory. By  claiming  to  stand  in  the  same  relations,  these 
terms  become  rivals,  as  it  were,  and  exclude  each  other.  But  a 
knowledge  of  the  particular  facts  involved  is  always  necessary 
in  order  to  determine  whether  or  not  two  assertions  are  really 
incompatible. 

§  8 1.  The  Law  of  Excluded  Middle.  —  The  third  law  is 
a  corollary  from  what  has  just  been  said  in  the  last  sec- 
tion. There  is  no  middle  ground,  it  declares,  between 
contradictories.  A  is  cither  b  or  not-b.  To  affirm  the 
one  is  to  deny  the  other.  When  we  have  real  contra- 
dictories,—  /.t'.,  when  not-b  is  not  merely  something 
different  from  b,  but  something  which  excludes  it,  — 
every  judgment  is  double-edged,  and  both  affirms  and 
denies  at  the  same  time.  To  deny  that  the  throw  of  a 
penny  has  given  heads,  is  to  assert  that  it  has  fallen 
tails.  As  we  have  seen,  however,  logic  affords  no  rules 
of  deciding  when  things  do  thus  stand  in  the  relation 
of  mutual  opposition.  The  law  of  Tlxcludcd  Middle 
states  only  that  tvJicrc  this  relation  does  exist,  ev^ery 
proposition  has  a  double  value,  and  both  affirms  and 
denies  at  the  same  time.  It  requires  special  know- 
ledge of  the  particular  facts  in  each  case  to  enable 
us  to  decide  what  things  are  thus  opposed  to  one 
another.  There  is  no  logical  law  by  means  of  which 
things  may  be  divided  into  two  opposing  groups  or 
classes. 


\ 

i 

i! 

f 

f 

pi 

* 

4 

Ml 

i     ■ 

't 

1-' 


11 


./, 


I     ii 


298 


THE   LAWS  OF  THOUGHT 


r 


tb  I 


;.  I  , 


It  is  important  to  notice  that  all  of  the  judgments 
which  we  use  in  everyday  life  are  to  some  extent  double- 
edged.  That  is,  they  contain,  besides  what  is  directly 
af^rmed,  some  implication  or  counter  statement.  For 
example,  to  say,  'that  object  is  red,'  is  implicitly  to  deny 
that  it  is  blue,  or  any  other  colour.  The  statement,  '  A 
never  looks  at  a  book,'  carries  with  it  the  implication 
that  A  is  not  very  intelligent.  In  almost  any  field 
where  we  have  any  systematic  knowledge,  we  can  limit 
pretty  definitely  the  number  of  possibilities — a  must 
be  either  /;,  or  c,  or  d.  In  such  cases,  to  affirm  that  a  is 
d,  is  of  course  to  deny  implicitly  c  and  d ;  and  con- 
versely, the  denial  of  any  one  possibility,  as  c,  enables 
one  to  assert  that  a  is  d  ov  d.  In  ordinary  conversa- 
tion, misunderstandings  and  misconceptions  frequently 
arise  because  neither  party  is  fully  aware  of  all  the  pos- 
sible cases  and  the  relation  between  them.  It  is  very 
difficult,  however,  to  make  a  statement  which  will  have 
no  counter  implications.  If  one  says,  '  this  railway  sys- 
tem does  not  employ  steam  power,'  the  proposition 
seems  to  justify  the  question:  'Does  it  then  use  elec- 
tricity or  compressed  air  ? '  We  should  feel  that  it  was 
a  mere  quibble  if  the  person  who  made  the  statement 
should  reply :  *  I  did  not  say  that  it  employed  any  kind 
of  power.'  'There  are  some  small  errors  in  this  paper,' 
would  ordinarily  be  taken  to  imply  the  counter  propo- 
sition, 'the  paper  contains  no  serious  errors.'  It  is 
clear  that  it  is  only  when  one's  knowledge  becomes 
systematic,  —  i.e.,  when  one  knows  the  relations  in 
which  all  the  facts  in  the  field  under  consideration 
stand   to   each   other,  —  that    one   can    be   fully  aware 


I 


judgments 
tent  clouble- 
:  is  directly 
ment.     For 
:itly  to  deny 
itement,  '  A 
implication 
it   any  field 
jQ  can  limit 
is  —  a  must 
rm  that  a  is 
';   and  con- 
is  c,  enables 
ry  conversa- 
3  frequently 
:  all  the  pos- 
.     It  is  very 
:h  will  have 
railway  sys- 
proposition 
m  use  elec- 
that  it  was 
statement 
id  any  kind 
this  paper,' 
nter  propo- 
ors.'      It  is 
2:e  becomes 
relations    in 
onsideration 
fully  aware 


§8i.    THE   LAW  OF   EXCLUDED    \".IDDLE 


299 


of  what  is   really  implied    in   each  assertion   or   denial 
(cf.  §§  41,  78). 

References 

F.  H.  Bradley,  T/ie  Principles  o/Loi^ic,  pp.  131-154,  343-360. 

B.  Bosanquet,  Logic,  Vol,  II.,  pp.  207-212. 

W.  S.  Jevons,  lilcmcntary  Lessons  in  Logic,  Ch.  XIV. 
"    "        "        77/6'  /Principles  of  Science,  Introduction. 

G.  T.  Ladd,  T/ie  Philosophy  of  Knotoledge,  Ch.  IX. 

C.  Sigvvart,  Logic,  %%  23-25. 

J.  Watson,  '"  The  Metaphysic  of  Aristotle,"  Philos.  Review,  Vol. 

VII.,  pp.  113-134- 


'I- El 


'«. 


* . 

ii  ■'  I. 


I  V 


\'%  I 


CHAPTER   XXIII 


TYPES    OF   JUDGMENT 


'i      ! 


ill 


II 


§  82.  Judgments  of  Quality.  —  Wc  have  hitherto  been 
considering  the  nature  of  Judgment  in  general,  and 
have  learned  something  regarding  its  main  character- 
istics. It  is  now  necessary  to  examine  briefly  some  of 
the  more  important  forms  or  types  of  Judgment.  We 
shall  begin  with  very  simple  and  elementary  ways  of 
judging,  and  afterwards  consider  some  of  the  more 
complex  types.  In  this  way,  we  shall  see  the  nature 
and  structure  of  Judgment  illustrated  at  different  levels 
of  thought.  And  we  also  hope  to  show  that  there  are 
no  arbitrary  divisions  in  the  process  of  thinking,  that 
the  lower  forms  of  Judgment  gradually  develop  into  the 
higher  in  accordance  with  the  general  law  of  evolution. 
It  is,  of  course,  impossible  to  cany  out  at  present  this 
plan  in  detail,  for  that  would  be  to  give  a  complete  his- 
tory of  the  development  of  thought.  It  will  be  neces- 
sary for  us  to  take  long  steps,  and  content  ourselves 
with  a  general  view  of  the  relation  of  the  various  stages 
in  the  development  of  Judgment. 

The  first  efforts  of  intelligence  to  understand  the 
world  take  the  form  of  judgments  of  Quality.  At  a  low 
stage  of  mental  development,  it  is  the  simple  qualities 
of  things  which  force  themselves  on  attention.  The 
young    child,    for  example,    takes    notice   of    only   the 

300 


§82.    JUDGMKNTS   OK  (QUALITY 


301 


therto  been 
eneral,  and 
1  character- 
:fly  some  of 
mcnt.  We 
try  ways  of 
:  the  more 
the  nature 
erent  levels 
it  there  are 
inking,  that 
lop  into  the 
f  evolution, 
present  this 
)mplete  his- 
1  be  neces- 
t  ourselves 


nous  stages 


^rstand  the 
At  a  low 
>le  qualities 
ition.  The 
:    only   the 


most  striking  qualities  of  things.  Ilis  judgments  are 
very  vague  and  indefinite,  and  take  account  only  of 
some  prominent  quality  of  things.  Tiiat  is,  there  is  no 
discrimination  of  the  various  parts  and  relations  of  the 
objects,  but  the  judgments  express  merely  a  general 
impression  based  upon  some  striking  quality.  Thus  it 
has  often  been  noticed  that  the  child  calls  every  man 
'papa,'  and  any  light,  of  whatever  size,  the  moon.  A 
little  boy,  known  to  the  author,  used  to  call  Sisters 
of  Charity,  crows,  on  account  of  the  colour  of  their 
dresses.  The  objects  as  he  apprehended  them  were 
simply  black,  and  nothing  more.  His  intelligence 
rested  in  the  qualitative  total  impression ;  the  vari- 
ous parts,  with  their  quantitative  relations,  which  he 
afterwards  learned  to  know  and  distinguish,  did  not 
at  that  time  exist  for  him. 

It  is  perhaps  impossible  to  find  in  the  experience  of 
an  adult  any  judgments  which  deal  entirely  with  simple 
qualities,  and  which  take  no  account  of  the  numbers,  and 
even  to  some  extent  of  the  relationp,  of  the  parts.  But 
we  can  find  examples  of  judgment  where  the  qualitative 
aspect  is  much  the  most  prominent  —  where  indeed  the 
quantitative  and  more  complex  relations  are  scarcely 
noticed  at  all.  *  This  is  green,'  *  that  is  a  strange  odour,' 
'there  is  something  a  long  way  off,'  — all  these  seem  to 
be  judgments  of  quality  or  general  impression,  and  to 
involve  scarcely  any  other  element.  It  is,  too,  the 
easiest  kind  of  judgment  to  make,  the  judgment  which 
involves  least  mental  effort,  and  which  notices  only 
the  most  evident,  and,  as  it  may  be  seen,  the  most 
superficial,  aspect  of  things.     It  is  evident  that  such 


i 


!  I     t 


'I'  It' 


s 


m 

ill 

^r    *■ 

i( 

1. 

1 

If    - 

>^           ,M,     , 

1 

'»<  < 


■)!l 


•i^' 


ill 


I 


iv 


'  -I 


■a 


302 


lYPKS   OK   JUDGMKNT 


judgments  belong  to  a  lower  stage  of  thinking,  than 
those  which  imply  analysis  and  perception  of  quantita- 
tive relations.  Compare,  for  example,  'this  is  very 
large,'  with,  'this  object  is  made  up  of  roots,  trunk, 
branches,  and  leaves  '  ;  or  'this  is  green,'  with,  'this  leaf 
is  divided  into  two  parts  by  a  rib  running  tiirough  the 
centre.'  The  first  judgment  in  each  pair  ol)viously 
involves  much  less  intellectual  work  than  the  latter. 
The  judgment  of  simple  quality  is,  as  we  have  seen,  the 
starting-point  of  thought.  It  is  with  this  kind  of 
thinking  that  the  knowledge  of  the  child  begins.  And, 
before  the  savage  learns  to  count,  ?'.<•.,  to  distinguish 
and  enumerate  the  parts  of  the  objects  with  which  he 
deals,  his  judgments  must  necessarily  belong  to  this 
same  type. 

It  must  never  be  forgotten,  however,  that  simple 
judgments  of  quality  are  really  judgments;  t'.c,  are  not 
given  to  the  mind  from  any  external  source,  but  are  the 
products  of  its  own  activity.  A  judgment,  as  we  have 
already  pointed  out  (§  /^),  implies  a  reaction  on  the 
part  of  the  mind  on  what  is  presented  to  consciousness 
through  the  senses.  It  distinguishes  and  puts  together 
the  material  which  sense  presei  '"■^  in  such  a  way  as  to 
perceive  its  significance  —  what  it  really  amounts  to  — 
as  a  piece  of  knowledge.  This  act  of  interpretative 
intelligence  has  gone,  however,  but  a  little  way  in  the 
type  of  judgment  with  which  we  are  dealing.  But  even 
in  a  vague  qualitative  judgment  like,  'there  is  something 
black,'  the  essential  characteristics  of  Judgment  can  be 
already  distinguished.  For  it  presupposes  at  least  some 
analysis  or  discrimination  of  the  black  object  from  the 


m;i 


rl 


§  82.     JUDGMENTS  OF  QUALIIV 


303 


1' 


iking,  than 
of  quantita- 
lis  is  very 
lots,  trunk, 
h,  •  this  leaf 
:liroiigh  the 
r   obviously 

the  latter. 
^e  seen,  the 
lis  kind  of 
:;ins.     And, 

distin^^uish 
:h  which  he 
ong  to  this 

hat  simple 
i.e.,  are  not 
but  are  the 
as  we  have 
ion  on  the 
nsciousness 
Its  together 
a  way  as  to 
lounts  to  — 
terpretative 

way  in  the 

But  even 

>  something 

lent  can  be 

least  some 
:t  from  the 


rest  of  the  environment,  and  of  the  black  colour  from 
other  colours.  And  the  judgment,  'something  is  black,' 
has  made  at  the  same  time  a  beginning  in  constiucting 
this  vague  something  into  a  system  of  qualities,  or  into  a 
thing  that  is  known.  The  other  qualities  and  relations 
are  as  yet  wrapped  up  in  the  indefiiniteness  of  the  'some- 
thing.' In  spite  of  its  indefiniteness,  however,  the  latter 
plays  the  part  of  a  permanent  centre  or  identity,.  It  is 
the  whole  from  which  the  quality  of  blackness  has  been 
separated  out,  and  to  which  it  is  again  attached. 

Our  thought,  however,  is  not  satisfied  with  a  know- 
ledge of  the  general  qualities  of  things,  but  pushes 
farther  its  work  of  analysis  and  construction.  In  this 
way,  it  begins  to  distinguish  the  various  parts  of  objects, 
and  to  compare  one  with  another.  We  not  only  judge 
that  'the  grass  is  green,'  but  go  further  and  say  'this 
piece  is  dark  green,  and  that  light  green.'  The  indefinite 
judgment,  'this  cane  is  heavy,'  is  no  longer  satisfactory, 
and  is  replaced  by,  '  this  end  of  the  cane  is  much 
heavier  than  that.'  And  when  this  stage  is  reached, 
judgments  of  Quality  are  already  passing  into  the  next 
higher  type,  judgments  of  Quantity.  For  the  moment 
of  comparison,  which  is  already  contained  in  these 
judgments,  is  the  basis  of  counting,  measuring,  and  all 
quantitative  determination.  In  advancing  from  the 
simple  apprehension  of  quality,  to  take  note  of,  and 
compare,  the  degree  or  intensity  which  the  same  quality 
manifests  yi  different  instances,  intelligence  has  entered 
upon  a  path  which  leads  directly  to  judgments  of 
quantity.  To  distinguish  parts,  to  regard  things  as 
degrees  or  instances  of   a  common  quality,  is  at  once 


A 


\ 


304 


TYPES  OF  JUDGMENT 


.•ij 


[i    I 


I 


^ii^i 


!' 


to  suggest    the    quantitative    process  of   counting  and 
measurement. 

§  83.  Judgments  of  Quantity.  —  It  is  very  difficult,  as 
we  have  seen,  to  draw  a  hard  and  fast  line  between 
quality  and  quantity.  Indefinite  judgments  of  general 
impression  which  do  not  imply  any  comparison,  seem 
always  to  be  qualitative  rather  than  quantitative  in 
character.  This  is  true,  I  think,  of  judgments  like, 
'this  object  is  very  large,'  'there  was  a  great  flock  of 
sheep  in  the  field.'  In  such  cases,  the  interest  does  not 
see*:!  to  be  quantitative  at  all ;  i.e.,  there  is  no  effort 
made  to  determine  hoiv  many  units  or  parts  there  are  in 
the  whole  about  which  the  judgment  is  made.  But  the 
general  impression  of  size  or  number  is  apprehended 
and  judged  of  at  the  same  level  of  intelligence,  and  in 
the  same  vague  way,  as  the  simple  qualities  with  which 
we  dealt  in  the  last  section.  It  is  by  means  of  such 
a  general  qualitative  impression  that  the  savage  who 
cannot  count  beyond  five,  is  able  to  distinguish  between 
six  and  some  larger  number.  And  we  must  suppose 
that  the  shepherd's  dog  does  not  learn  that  some  of  the 
sheep  are  missing  by  any  process  of  counting.  We 
must  suppose  that  the  general  qualitative  impression 
made  by  the  smaller  flock  is  different  from  that  made  by 
the  larger,  and  that  there  has  been  no  real  counting  or 
estimation  of  number  in  the  case. 

But  quantitative  judgments  proper  belong  to  a  higher 
stage  of  intelligence  than  do  those  which  have  just 
been  described.  Indefinite  judgments,  like  '  this  is  very 
large,'  or,  'there  are  a  great  many  stars  in  that  group,' 


)unting  and 


T  difficult,  as 
ine  between 
3  of  general 
arison,  seem 
mtitative  in 
jments  like, 
'eat  flock  of 
•est  does  not 
is  no  effort 

there  are  in 
ie.  But  the 
apprehended 
ence,  and  in 
5  with  which 
ans  of  such 

savaofe  who 

ish  between 
just   suppose 

some  of  the 
We 
impression 

lat  made  by 


mtmg. 


Icountuig  or 


to  a  higher 

have  just 

this  is  very 

[that  group,' 


§  83.     JUDGMENTS   OF   QUANlll Y 


305 


are  not  satisfactory  pieces  of  knowledge.  We  accord- 
ingly set  ourselves  to  get  more  exact  information  about 
the  parts  which  compose  the  wholes.  The  first  step 
in  this  process  leads  to  Judgments  of  Eninncmtion.  If 
the  whole  which  is  analyzed  is  composed  of  homogene- 
ous parts,  the  judgments  of  enumeration  take  the  form 
of  simple  counting.  'There  are  one,  two,  three,  .  .  . 
twenty  men  in  this  company.'  Where  the  parts  are 
not  of  the  same  kind,  however,  a  separate  name  may 
have  to  be  given  to  each.  *  This  plant  is  composed  of 
root,  stalk,  leaves,  and  flower.' 

But  exact  quantitative  knowledge  requires  us  to  do 
more  than  enumerate  the  parts  of  which  a  whole  is 
composed.  We  must  go  on  and  wcigJi  or  measure 
them.  There  is  of  course  no  essential  difference  be- 
tween weighing  and  measuring,  so  that  we  may  call 
all  judgments  which  express  the  result  of  this  process 
Judgments  of  Measure.  It  is  worth  noting  that  judg- 
ments of  this  class  are  not  so  simple  and  direct  as  may 
appear  at  first  sight.  When  we  measure,  we  express 
the  relation  of  the  parts  with  which  we  are  dealing  to 
some  common  unit  or  standard.  The  judgment,  'this 
tower  is  200  feet  high,'  means  that  if  the  tower  is  com- 
pared with  a  foot-rule,  it  will  be  found  to  contain  it 
200  times.  It  really,  then,  involves  a  proportion,  and 
might  be  expressed  :-  tower  :  foot-rule  =  200  :  i. 

The  point  which  it  is  important  to  notice  is  that  all 
measurement  is  the  result  of  comparison.  In  the  first 
place,  some  unit  is  more  or  less  arbitrarily  selected. 
Then  the  judgment  states  simply  the  relation  between 
this  unit  and  the  object  measured  :  one  is  contained  in 

X 


;.    'J 


'•(,'. 


\s\ 


i 


i<(l     li 


ill 

m 
k 


.  ■ :  [■ 


Kii 


■  I 


M 


\*i 


306 


TYPES   OF   JUDGMENT 


the  other  once,  or  twice,  or  ten  times.  The  quantita- 
tive determination  thus  obtained,  then,  is  merely  rela- 
tive. That  is,  it  does  not  belong  absolutely,  and  in  its 
own  right  to  the  object  measured,  d/it  indicates  tJie 
rclatio7i  of  that  object  to  something  else. 

For  this  reason,  it  may  seem  that  quantitative  rela- 
tions tell  us  nothing  regarding  the  real  nature  of 
objects,  and  that  to  discover  what  the  latter  are  in 
themsekfes,  we  shall  have  to  return  to  the  point  of  view 
of  quality.  But  we  have  seen  that  simple  judgments  of 
quality  yield  a  very  unsatisfactory  kind  of  knowledge. 
Moreover,  we  should  find  on  examination  that  even 
qualities  always  imply  a  reference  to  each  other,  and 
are  no  more  absolute  than  quantities. 

In  order  to  obtain  more  satisfactory  knowledge  re- 
garding things,  we  shall  have  to  go  forward  to  a  higher 
type  of  judgment,  rather  than  backward  to  quality. 
But  the  importance  of  quantitative  determination  for 
exact  knowledge  must  not  be  overlooked.  By  means 
of  measurement,  things  are  reduced  to  common  terms, 
as  it  were,  and  thus  a  basis  of  comparison  is  afforded 
where  it  would  otherwise  be  impossible.  To  reduce 
everything  to  such  a  common  measure  is  the  business 
of  the  physico-matbematical  sciences.  Everything  has 
a  quantitative  value,  and  can  be  expressed  mathemati- 
cally in  terms  of  some  unit  or  standard,  as,  for  exam- 
ple, the  unit  of  heat,  or  of  pressure,  or  the  electrical 
unit.  It  was  this  tendency  to  count  and  measure  and 
weigh  things  which  established  the  body  of  exact  know- 
ledge which  we  call  science.  And  in  almost  every  field, 
knowledge  increases  greatly,  both  in  extent  and  exact- 


le  quantita- 
rnerely  rela- 
^,  and  in  its 
idicatcs  the 

itative  rela- 

nature    of 

Ltter  are  in 

)int  of  view 

idgments  of 

knowledge. 

1   that  even 

other,  and 

owledge  re- 
to  a  higher 
to    quality. 

lination  for 
By  means 

imon  terms, 
is  afforded 
To  reduce 

he  business 
rything  has 
mathemati- 
,  for  exam- 
le  electrical 
leasure  and 
exact  know- 
every  field, 
and  exact- 


§84.     JUUGMENT.S   OF   CAUSAL   CONNECTION         307 

ness,  as  soon  as  it  is  found  possible  to  reduce  all  phe- 
nomena to  a  common  measure,  and  to  express  their 
relations   by   means  of  mathematical    formulas. 

It  is  a  great  step  in  advance  to  be  able  to  compare  things  as 
quantities,  and  to  express  their  relations  in  terms  of  number.  But 
judgments  of  quantity  are  not  entirely  satisfactory ;  they  are,  as  has 
already  been  noticed,  merely  relative  in  character.  Moreover,  from 
a  quantitative  point  of  view,  each  thing  is  equivalent  to  the  sum  of 
its  parts.  When  the  parts  have  been  enumerated  and  measured, 
the  value  of  the  whole  is  obtained  ))y  addition.  But  it  is  scarcely 
ever  possible  to  represent  adequately  the  nature  of  a  whole  in  this 
way.  So  long  as  we  ^re  dealing  with  a  piece  of  inorganic  matter, 
the  method  of  regarding  the  sum  of  the  parts  as  equivalent  to  the 
thing,  generally  gives  good  results  and  leads  to  nc  difficulty.  But  it 
is  quite  different  when  the  whole  in  question  belongs  to  something 
which  has  life  and  consciousness.  In  such  cases,  we  liave  what  has 
already  been  called  an  organic  whole  (§  78).  Now.  it  is  clear  that 
the  principle  of  quantity,  which  can  only  add  and  sul^tract,  is  in- 
sufficient to  represent  completely  the  nature  of  an  object  of  this  kind. 
It  has  no  means  of  repri,.senting  the  individuality  or  real  whole, 
which  rather  constitutes  the  parts,  than  is  constituted  by  them. 
That  is,  to  understand  such  objects,  we  shall  have  to  take  a  new 
point  of  view,  and  begin  with  the  whole  rather  than  with  the  parts. 
From  the  point  of  view  of  quantity,  the  nature  of  the  whole  is  dis- 
covered by  adding  together  the  parts ;  while  in  order  to  understand 
objects  which  possess  an  individuality  of  their  own,  there  seems  to 
be  a  central  principle  to  which  the  parts  are  subordinated,  and  in 
relation  to  whirh  alone  they  can  be  understood.  The  type  of  judg- 
ments which  deal  with  such  objects  we  shall  have  to  discuss  in 
§85. 

§  84.  Judgments  of  Causal  Connection.  —  Another  class 
of  judgments  used  in  l)uilding  up  knowledge,  may  be 
called  judgments  of  Causal  Connection.  They  under- 
take to  show  how  the  various  changes  which  go  on  in 


\  '"       I  ! 


M 


I   •  ■:  I 


1    !  *  I 


;,(, 


''r' 


\ 


308 


TYPES   OF  JUDGMENT 


'"\  \ 


1''*: 


things  arc  connected  causally  with  other  things  or 
events.  This  type  of  judgment — leading  as  it  does 
beyond  the  particular  object,  to  a  knowledge  of  the  ways 
in  which  objects  are  connected  —  seems  to  belong  to  a 
higher  stage  of  mental  development  than  those  which 
merely  take  note  of  quality  and  quantity.  This  does 
not  mean  that  we  never  look  for  causes,  until  the  quali- 
ties and  quantities  of  things  have  been  discovered.  Nor 
is  it  true  that  any  causal  judgment,  however  vague  and 
unsatisfactory,  is  higher  than  any  judgment  of  quality 
or  quantity  whatsoever.  But,  in  the  beginnings  of  know- 
ledge, one  may  say,  thought  does  not  travel  outside  the 
particular  object  to  show  the  connections  of  the  latter 
with  anything  else.  And  beginning  in  this  way,  it 
seizes  first  upon  quality  and  quantity  which  seem  to  be- 
long to  things  in  themselves.  We  have  seen,  however, 
that  as  a  matter  of  fact  judgments  of  quantity  involve 
comparison,  and  so  a  reference  of  one  thing  to  another, 
though  that  reference  is  not  usually  made  consciously 
or  explicitly.  But,  when  we  judge  that  one  thing  is 
causally  connected  with  another,  tlie  external  reference 
has  become  explicit,  and  is  the  very  essence  of  the  judg- 
ment. 

The  word  *  cause '  has  been  used  in  a  great  many 
senses,  and  its  various  meanings  have  gi\en  rise  to  a 
great  deal  of  discussion.  That  every  event  must  have 
a  cauac,  was  formerly  regarded  ,-  s  an  innate  truth,  or  a 
priori  proposition.  We  have  seen,  however,  that  we  do 
not  come  into  the  world  with  any  ready-made  stock  of 
knowledge.  All  knowledge,  we  have  often  repeated,  is 
the  result  of  the  mind's  own  judging  activity.     The  so- 


§  84.     JULXJMHNTS  OF  CAUSAL  CONNECTION         309 


things  or 
as  it  docs 
if  the  ways 
Dclong  to  a 
liosc  which 

This  does 
I  the  quali- 
cred.     Nor 

vague  and 

of  qiiahty 
^s  of  know- 
outside  the 
[  the  latter 
his  way,  it 
■ieem  to  be- 
1,  however, 
tity  involve 
to  another, 
consciously 
le  thing  is 
reference 

)f  the  judg- 

rcat  many 
rise  to  a 
must  have 
truth,  or  a 
that  we  do 
:le  stock  of 
■epeated,  is 
The  so- 


called  law  of  causation  (every  event  must  have  a  cause) 
must  therefore  express  the  fact  that  thought  does  con- 
nect things  as  causes  and  effects.  Intelligence  is  not 
satisfied  to  take  things  in  isolation  ;  it  tries  to  gain  an 
insight  into  the  ways  in  which  they  are  connected,  to 
discover  what  one  has  to  do  v/ith  another.  And  this  is 
just  the  characteristic  of  thought  which  was  emphasized 
in  §  78.  Judgment,  it  was  there  said,  is  a  process  of 
constructing  a  system,  of  showing  how  the  various  parts 
of  knowledge  fit  into  one  another,  and  are  mutually  de- 
pendent upon  one  another.  The  tendency  of  thought 
to  connect  things  causally,  then,  is  the  same  as  its  ten- 
dency towards  a  system,  which  has  now  become  more 
explicit  and  conscious  of  itself  in  this  type  of  judgment 
than  it  was  in  quality  and  quantity. 

It  will  be  interesting  to  note  some  of  the  most  impor- 
tant changes  which  take  place  in  the  principle  of  causal 
explanation  at  different  stages  in  the  development  of 
knowledge.  The  child  and  the  savage  regard  all 
changes  and  events  which  take  place  in  the  natural 
world,  as  due  to  the  agency  of  living  beings.  These 
beings  are  represented  as  more  or  less  similar  to  men, 
and  as  endowed  with  human  passions  and  emotions. 
Thus  we  say  that  the  earliest  kind  of  explanation  is  es- 
sentially anthropomorphic.  This  word  is  derived  from 
civOpcoTTo^i,  a  man,  and  ixop^i],  shape  or  form,  and  hence 
is  used  to  describe  the  way  of  representing  either  a 
spiritual  being,  as  for  example,  the  Deity,  or  natural 
forces  like  fire,  wind,  etc.,  in  human  form.  It  is  proba- 
bly true  that  at  a  very  early  stage  in  the  development 
of  both   the  individual  and   the  race,  every   object  is 


«*' 


'■^ 


:  i. 


3IO 


TYPES   OF  JUDGMENT 


i 


p 


'  1 


?( ' 


supposed  to  have  life.  Or,  perhaps,  it  would  be  truer  to 
say  that  the  young  child  (and  the  same  would  be  true 
for  the  savage  on  a  low  plane  of  intelligence)  has  not 
yet  made  the  distinction  between  animate  and  inani- 
mate objects,  but  vaguely  regards  everything  as  like 
himself.  This  stage  is  usually  known  as  animism^ 
because  each  object  is  supposed  to  be  endowed  with 
a  spirit,  or  aninia. 

Gradually,  however,  the  distinction  between  animate 
and  inanimate  objects  becomes  clear.  Accordingly, 
we  find  that  at  a  somewhat  more  advanced  stage  the 
mode  of  explanation  takes  a  different  form,  though 
it  is  still  anthropomorphic.  Physical  objects  are  no 
longer  regarded  as  living,  but  the  changes  in  them 
are  supposed  to  be  due  to  the  action  of  spirits,  who 
are  outside  of  the  objects,  but  who  use  them  to  ac- 
complish their  purposes.  These  invisible  spiritual 
agents,  to  whom  all  natural  events  are  referred,  have 
been  variously  named.  It  is  clear,  however,  that  the 
gods  of  mythology  belong  here,  as  well  as  the  fairies, 
elfs,  ghosts,  and  witches  of  the  popular  folk  stories. 
It  was  a  great  advance  when  a  Greek  thinker,  named 
Thalcs,  came  to  the  conclusion  that  it  does  not  in 
any  way  explain  natural  events  to  refer  them  to  the 
action  of  the  gods.  For,  in  the  first  place,  to  say  that 
the  gods  cause  this  or  that  event,  is  to  state  some- 
thing which  we  have  no  means  of  proving.  And  even 
if  the  assertion  were  true,  it  would  not  really  explain 
anything.  For  it  would  not  enable  us  to  understand 
lioiv  the  changes  in  question  came  about.  It  would 
tell  nothing  whatever  regarding  the  actual  steps  in  the 


n! 


X 


be  truer  to 
Id  be  true 
e)  has  not 
and  inani- 
ing  as  like 
animism, 
lowed  with 

sn  animate 
ccordinc^lv, 
I  stage  the 
m,    though 
:cts  are  no 
;s   in  them 
,pirits,  who 
bem   to  ac- 
e    spiritual 
3rred,  have 
r,  that  the 
the  fairies, 
oik  stories. 
^er,  named 
oes    not  in 
icm  to  the 
to  say  that 
tate  some- 
And  even 
illy  explain 
understand 
It  would 
teps  in  the 


§84.     JUDGMENTS  OF  CAUSAL  CONNECTIOX         311 

process  itself.  Thales  saw  this,  and  tried  to  give  a 
natural  explanation  of  the  world,  and  all  that  goes  on 
in  it.  He  tried  to  build  up  a  real  system  of  know- 
ledge by  attempting  to  show  how  everything  which  has 
happened  in  the  world  has  been  connected  with  some 
natural  cause.  We  know  very  little  about  the  actual 
explanation  of  the  world  which  Thales  gave,  except  that 
he  tried  to  derive  everything  from  water.  It  is  on  ac- 
count of  the  method  which  he  adopted,  rather  than  of 
what  he  actually  performed,  that  he  is  regarded  as  the 
founder  of  science.  Thales  first  showed,  one  may  say, 
that  knowledge  means  an  insight  into  the  ways  in  which 
the  actual  phenomena  of  the  world  are  connected.  We 
cannot  unite  into  a  system  things  so  different  in  kind 
as  spirits  and  natural  phenomena.  Or  we  may  say  that 
real  explanation  demands  that  there  shall  be  some  like- 
ness, or  ground  of  similarity,  between  the  cause  and  tht 
effect.  An  event  which  happens  ii  ':he  world  of  objects, 
must  be  explained  by  showing  its  connection  with  some 
other  event,  of  a  similar  character,  which  pr    ^"des  it. 

The  development  of  this  conception  of  scientific  ex- 
planation also  influenced  still  further  the  notion  of 
causality.  We  have  seen  that  in  the  beginnings  of 
knowledge  every  event  was  supposed  to  be  due  to  the 
action  of  some  living  agent,  or  spiritual  being.  Even 
after  this  mythological  mode  of  explanation  is  dis- 
carded, and  natural  causes  put  in  the  place  of  spirits, 
it  is' still  difficult  to  rid  oneself  entirely  of  the  old  an- 
thropomorphism. The  popular  mind  still  tends  to 
regard  the  cause  as  an  agent  which  produces  the  effect, 
through  some  power  or  efficiency  which  it  possesses.    It 


;  t 


V 

'1'  .i: 

iti' 

ii, 


i^B'*' 


i    i 


h  ' 


312 


TYPES   OF  JUDGMENT 


ic  not  necessary  to  raise  the  question  at  present  whether 
there  are  any  grounds  for  tliis  belief.  To  discuss  this 
problem  would  carry  us  beyond  logic  into  metai)hysics. 
What  we  wish  to  notice  is  that  science  has  gradually 
abandoned  the  notion  that  the  cause  (/(Us  sonictliini^  to 
the  effect.  That,  as  we  have  seen,  is  a  remnant  of  the 
old  prescicntific  idea,  and  a  notion  which  does  not  aid 
at  all  in  explaining  our  knowledge.  It  is  the  business 
of  science  to  show  Jiow  the  things  and  events  which 
make  up  our  experience  are  necessarily  connected  with 
one  other.  Science  has  to  discover  what  things  invari- 
ably go  along  with  one  another,  and  necessarily  pre- 
suppose one  another.  And,  when  it  is  found  that  some 
particular  thing  or  event,  A,  invariably  precedes  another 
particular  occurrence,  B,  the  former  is  regarded  as  the 
cause,  and  the  latter  as  the  effect.  In  order  to  elimi- 
nate as  far  as  possible  the  notion  of  agency  or  effi- 
ciency which  attaches  to  the  word  cause,  the  terms 
'antecedent'  and  'consequent'  are  often  used  to  in- 
dicate this  relation.  For  science,  the  cause  is  not  an 
active  agent,  but  the  invariable  antecedent  of  something 
else  which  simply  follows  j.t.  The  cause  does  not  explain 
the  effect  by  assigning  an  agent  which  brings  the  latter 
about  through  its  personal  efforts ;  but  it  explains, 
because  it  reveals  another  necessary  step  in  the  process, 
and  gives  us  a  new  fact  which  joins  on  or  can  be  con- 
nected with  the  one  from  which  we  start. 

We  conclude  then  that  the  cause  of  any  event  is  its 
invariable  and  necessary  antecedent.  In  another  part  of 
this  book  (Chs.  XV.,  XVI.),  it  is  shown  what  tests  it  is 
necessary  to  apply  in  order  to  determine  whether  two 


§84.     JUDGMENTS   OV  CAUSAL  COWKCPHW         313 


cnt  whether 
(Hscuss  this 
netaphysics. 
LS  gradually 
w//r//////i/-  to 
inant  of  the 
Joes  not  aid 
he  business 
/ents  which 
inected  with 
linsfs  invari- 
issarily  pre- 
id  that  some 
^les  another 
irded  as  the 
der  to  elimi- 
ncy  or  cffi- 
,  the  terms 
used  to  in- 
e  is  not  an 
f  somethinir 
not  explain 
js  the  latter 
it  explains, 
the  process, 
can  be  con- 
event  is  its 
)ther  part  of 
it  tests  it  is 
whether  two 


pi 


cnomcna  arc  merely  accidentally  conjoined,  or  whether 
the  connection  is  essential  and  real.  It  is  necessary  now 
to  take  one  more  stop  in  tracing;  the  various  ways  in 
which  the  idea  of  causality  has  been  used.  As  a  re- 
sult of  a  famous  scientific  discovery,  which  was  made 
about  the  middle  of  the  present  century,  a  new  element 
has  been  added  to  the  notion  of  cause  in  its  application 
to  physical  phenomena.  The  law  of  the  Conservation 
of  Energy  states  that  the  amount  of  energy,  or  {)ower  of 
doing  work,  possessed  by  any  set  of  bodies,  remains  con- 
stant. Any  change  in  a  material  body  is  the  result  of 
a  transformation  of  energy  from  one  forni  to  another. 
The  same  is  ti  uc  of  the  world  as  a  whole  :  the  total 
amount  of  energy  which  it  contains  remains  constant. 
All  changes  which  take  place  in  the  physical  universe 
—  motion  into  heat,  or  electricity  into  motion  — are  sim- 
ply different  forms,  or  manifestations,  of  the  one  world- 
energy. 

As  a  result  of  this  law,  the  effect  always  represents 
the  same  amount  of  energy,  or  power  of  doing  work, 
as  the  cause.  Since  no  energy  is  ever  lost,  the  one 
must  be  equal  to  the  other.  And,  as  a  matter  of  fact, 
the  quantitative  equivalence  of  many  of  the  various  forms 
of  energy  has  been  proved  by  actual  measurement.  In 
working  out  this  law,  for  example,  Joule  showed  that 
"the  energy  stored  up  in  the  i  lb.  weight  which  had  been 
pulled  up  772  feet  was  graduallv  transformed,  as  soon  as 
the  weight  was  reh^ased,  into  an  amount  of  heat  capable 
of  raising  the  temperature  of  a  pound  of  water  1° 
Fahr. ;  while  Hirn  showed,  on  the  other  hand,  that  ex- 
actly this  amount  of  heat  would,  if  it  could  be  turned 


Vf, 


\-l    ■!. 


;  , 


•t  '        I 


lli^ 


314 


TVPKS   OF  JUDdMEXr 


tJ^ 


t!'! 


■P '' 


.1. 


S' 


I  1 


i 


back  again  into  energy,  raise  tlie  i  lb.  weight  to  the 
height  of  772  feet  at  which  it  stood  before."  ' 

The  new  element  which  this  law  adds  to  the  idea  of 
cause  as  a  necessary  and  invariable  antecedent,  is  that  of 
the  quantitative  identity  of  cause  and  effect.  Taking  the 
phenomena  which  are  connected  in  this  way  to  repre- 
sent simply  certain  quantities  of  energy,  we  say  that  the 
one  is  equivalent  to  the  other.  The  energy  which  the 
cause  represents  has  been  transformed  without  loss,  and 
reappears  in  the  effect.  If  what  seems  to  be  the  total 
effect  is  not  cqu  ..1  to  the  cause,  part  of  the  energy  of 
the  latter  must  have  been  transformed  into  something 
else.     No  energy  can  have  been  lost. 

It  becomes,  therefore,  the  task  of  the  physical  sci- 
ences to  show  that  this  relation  of  quantitative  identity 
exists  between  phenomena  which  are  causally  connected. 
The  ideal  of  physical  science,  is  to  prove  that  two  phe- 
nomena arc  connected  as  cause  and  effect,  by  showing 
that  both  represent  the  same  quantity  of  energy.  For 
this  purpose,  measurement  and  calculation  are  neces- 
sary. The  physical  sciences,  as  was  pointed  out  in  the 
last  section,  deal  largely  with  judgments  of  quantity, 
and  devote  themselves  to  showing  by  measurement  that 
the  same  amount  of  energy  persists  through  the  various 
changes  which  phenomena  undergo.  In  establishing 
causal  connections,  the  physical  sciences  find  it  necessary 
to  use  the  principles  of  measurement  and  calculation. 

It  will  be  evident,  from  what  has  been  already  stated,  that  this 
relation  of  cause  and  effect  should  apply  to  all  phenomena  whose 

1  Buckley,  S/ior/  History  of  Natural  Science^  p.  339. 


Ijjjht  to  the 
1 

the  idea  of 
\t,  is  that  of 

Taking  the 
ly  to  repre- 
say  that  the 
y  which  the 
Hit  loss,  and 
be  the  total 
2  energy  of 
)  something 

)hysical  sci- 

;ive  identity 

r  connected. 

at  two  phe- 

by  showing 

ergy.     For 

are  neces- 

oiit  in  the 

quantity, 

ement  that 

the  various 

stablishing 

t  necessary 

culation. 

ted,  that  this 
)inena  whose 

139- 


§85.     JUDGMKNTS  OV   IXDIVinUAI,!  IV 


315 


II 


energy  is  capable  of  heing  measure  d  rc[)rc.scntetl  in  quantitative 
terms.  As  a  matter  of  fact,  however,  the  law  has  been  proved  only 
in  physics  and  chemistry.  From  the  very  nature  of  the  case,  it  is 
extremely  difficult  to  measure  exactly  the  relations  of  cause  and  etVect 
in  the  sciences  which  deal  with  organic  life.  Hut  even  in  those 
sciences,  the  law  of  the  Conservation  of  Enerj^y  is  assumed  to  hold 
true.  For  example,  the  amount  of  energy  which  a  plant  contains,  is 
assumed  to  be  exactly  the  same  as  that  represented  by  the  various 
elements  or  forces  —  water,  sunlight,  mineral  substances,  etc. — 
which  were  instrumental  in  composing  it.  In  the  same  way,  we 
suppose  that  the  same  relation  hokls  of  the  chan<fes  which  go  on 
in  the  brain,  though  we  are,  of  course,  unable  to  prove  this  by 
actual  measurement. 

It  is  difficult,  however,  to  see  how  this  law  can  have  any  applica- 
tion to  mental  phenomena.  We  can  indeed  measure  the  intensity 
and  duration  of  sensations.  IJut  neither  feelings  nor  complex  pro- 
cesses of  mind  seem  to  be  capable  of  measurement.  Moreover,  it  is 
never  possible  to  measure  the  energy,  or  power  of  doing  work,  which 
states  of  consciousness  possess,  and  to  equate  one  with  another  in 
this  respect.  And  this  being  so,  the  law  of  the  Conservation  of 
Energy  cannot,  of  course,  apply  to  psychical  causes  and  effects.  In 
the  mental  sciences,  then,  we  cannot  claim  that  the  notion  of  Cau- 
sality contains  the  element  of  quantitative  identity  between  cause 
and  effect  which  has  been  found  to  exist  in  the  physical  sciences.^ 

§  85.  Judgments  of  Individuality.  —  By  Judgments  of 
Individuality,  we  mean  judgments  which  regard  some 
complex  object  as  a  real  whole  with  a  definite  nature  of 
its  own.  We  have  already  had  occasion  (§  78)  to  dis- 
tinguish a  mere  aggregate  or  sum  of  parts,  like  a  heap 
of  stones,  from  a  true  whole  which  possesses  a  certain 
character  and  individuality  of  its  own.  It  is  the  former 
point  of  view  from  which  judgments  of  quantity  and 

1  Cf.  Wuiult,  Et/iik  (ist  ed.)  pp.  398  f.;   Sigwart,  Logic,  §  97^/,  7. 


'■  ', 


,!"     —Ml- 


316 


TYri:S  oi-   JUDGMENT 


H 


if 


of  causal  connection  rccjanl  objects.  For  these  types  of 
jii(lj;ments  are  concerned  wholly  with  the  parts  —  the 
former  to  measure,  and  the  latter  to  show  their  causal 
connection.  It  requires  a  new  form  of  judgment  to 
represent  adequately  the  nature  of  a  complex  object 
which  possesses  individuality.  This  form  gives  expres- 
sion to  the  organic  unity  and  wholeness  of  things,  and 
emphasizes  the  way  in  which  the  parts  cooperate  for  a 
common  purpose  or  end.  Thus  vvc  regard  the  parts  of 
a  plant  as  a  unity  cooperating  in  a  common  purpose, 
and  a  man  as  a  conscious  system  of  ends. 

(i)  We  have  seen  that  jiulj^iiicnts  of  causal  connection  relate  phe- 
nomena as  causes  and  effects.  A  chanti^e  in  an  object  is  explained 
by  showing  that  some  other  change  or  event  invariably  precedes  it. 
But  this  chanije.  in  its  turn,  demands  explanation,  and  has  to  be 
accounted  for  by  the  discovery  of  a  new  cause.  This  type  of  judg- 
ment shows  that  one  phenomenon  is  connected  with  a  second,  and 
a  second  with  a  third,  and  so  on  indefinitely.  The  view  of  the 
world  wiiich  it  presents  is  that  of  a  never-ending  series  of  causes 
and  eflfects.  It  is  never  possible  to  find  a  cause  which  is  not  itself 
the  effect  of  something  else  No  phenomenon  possesses  any  inde- 
pendence of  its  own,  but  is  simply  a  link  in  a  series,  or  a  piece  of 
a  whole  that  is  never  completed. 

In  the  last  section,  it  was  stated  that  causal  judcjments  connect 
one  part  of  our  knowledge  with  another,  and,  in  this  way,  aid  in 
uniting  the  parts  of  our  experience  in  a  systematic  way.  Now  it 
is  undoubtedly  true  that  it  would  be  impossible  to  have  any  real 
knowledge  of  anything  as  a  whole,  or  an  individual,  without  know- 
ing the  way  in  which  the  parts  are  related,  and  mutually  depend 
upon  each  other.  In  that  sense,  jud<j;ments  of  causal  relation  arc 
indispensable  to  a  knowledge  of  a  true  whole.  But  this  form  of 
judgment  itself  resolutely  goes  on  connecting  part  with  part  —  one 
phenomenon  with  another  —  and  refuses  to  regard  any  ejroup  of 
parts  as  possessed  of  an   independent   character  or  individuality. 


•        1 


§85.    JUDGMENTS  OF   INDWIDUAI.rrV 


317 


!se  types  of 
larts  —  the 
heir  causal 
(Igment  to 
:)lex  object 
ves  cxpres- 
things,  and 
lerate  for  a 
;lie  parts  of 
111  purpose, 

on  relate  phe- 
t  is  explained 
y  precedes  it. 
nd  has  to  be 
type  of  judg- 
1  second,  and 
:  view  of  the 
■ies  of  causes 
h  is  not  itself 
iscs  any  inde- 
or  a  piece  of 

lents  connect 
,  way,  aid  in 
/ay.  Now  it 
lave  any  real 

thout  know- 
ually  depend 
1  relation  are 

this  form  of 
;h  part  —  one 
my  group  of 
individuality. 


From  lliis  point  of  \ie\v,  everything  is  externally  deteriniiicd  ;  its 
cause,  or  principle  of  explanation,  lies  outside  of  it  in  something 
else.  The  mark  of  individuality,  on  the  other  hanil,  is  the  power 
of  origination,  or  self-determination. 

(2)  I'sychology,  one  may  say,  adopts  the  standpoint  of  Causal 
Connection;  Ethics,  that  of  individuality.  Tiie  former  science  re- 
gards mind  as  a  s///u  of  mental  processes,  and  uiulcrtakes  to  show 
how  its  various  i)arts  are  connected.  Every  state  of  consciousness 
is  supposed  to  be  determined  by  something  external  to  itself — some 
antecedent  mental  state,  or  some  bodily  process.  The  interest,  as 
was  previously  said,  is  centred  in  the  parts,  and  it  is  very  rarely  that 
the  psychologist  stops  to  look  at  the  mind  as  a  whole.  Ethics,  on 
the  other  hand,  has  to  begin  with  the  individual.  It  does  not  regard 
mind  as  a  thing  or  substance  (that  is  the  naive  point  of  view  against 
which  psychology  rightly  warns  us),  but  as  a  self-conscious  system 
of  ideas,  purposes,  and  feelings,  wliich  jiossesses  the  power  of  initia- 
ting action,  and  of  determining  itself.  Ethics  can  adopt  all  that  psy- 
chology has  to  tell  regarding  the  mechanism  of  the  mental  jirocesses. 
Indeed,  without  a  systematic  and  detailed  account  of  the  nature  and 
laws  of  mental  life  it  (  uld  have  no  adequate  conception  of  mind 
as  a  whole :  the  judgment  of  Individuality  must  use  the  results  of 
judgments  of  Causal  Connection.  What  it  really  does,  is  to  trans- 
form the  s/p//  of  mental  processes  into  a  system  which  has  a  real 
unity  of  its  own.  For  it  is  only  when  a  person  is  regarded  as  a 
self-conscious  and  self-acting  individual,  that  he  can  be  supposed 
capable  of  conduct  to  which  the  terms  *  moral '  and  *  inunoral '  can 
properly  be  applied. 

References 

Hegel,  Lof^ic^  Pt.  II.,  The  Doctrine  of  Essence  (Wallace's  trans., 
2d  ed.),  pp.  206-2S6. 

B.  Bosanquet,  Loi^ic,  Vol.  I.  Chs.  II. -V. 
J.  S.  Mill,  Loi^ic,  Bk.  III.  Ch.  V. 

C.  Sigwart,  Logic,  §  73. 


CHAPTER    XXIV 


THE     NATURE     OF     INFERENCE. 

DEDUCTION 


INDUCTION     AND 


§  86.  Judgment  and  Inference.  —  It  must  not  be  for- 
gotten that  our  object  in  these  chapters  is  to  obtain  as 
definite  a  conception  as  possible  regarding  the  nature  of 
thought.  To  attain  this  end,  we  agreed  (§  73)  that 
it  would  be  advantageous  to  begin  with  the  simplest  or 
most  elementary  form  of  thinking.  That  form  we  found 
to  be  Judgment.  We  have  now  endeavoured  to  show 
what  Judgment  is,  and  what  part  it  plays  in  building  up 
knowledge.  And,  in  the  last  chapter,  we  have  attempted 
to  see  some  of  the  steps  in  the  evolution  of  Judgment, 
as  it  passes  from  simple  judgments  of  Quality  to  judg- 
ments of  Individuality.  This  account  being  completed, 
it  remains  now  to  discuss  the  nature  of  reasoning  or 
Inference. 

We  shall  probably  get  the  clearest  idea  of  the  nature 
of  Inference  by  regarding  it  as  a  completely  developed 
judgment.  As  thinking  develops  from  the  form  of  sim- 
ple judgment  to  that  of  Inference,  it  displays  progressive 
differentiation  and  integration.  In  accordance  with  this 
law,  we  can  say  (i)that  Inference  is  more  complex  than 
Judgment.  The  latter  process,  in  its  simplest  form,  can 
scarcely  be  said  to  have  any  parts  :  it  represents  a  single 
act  or  pulsation  of  intelligence.     Inference,  on  the  other 

318 


'ION     AND 

t  not  be  for- 
to  obtain  as 
the  nature  of 
(§  73)  that 
5  simplest  or 
)rm  we  found 
ired  to  show 
1  building  up 
ve  attempted 
>f  Judgment, 
ility  to  judg- 
g  completed, 
reasoning  or 

f  the  nature 
ly  developed 
form  of  sim- 
s  progressive 
nee  with  this 
:omplex  than 
est  form,  can 
cuts  a  single 
on  the  other 


§  86.     JUDGMENT   AND    INFERENCE 


319 


hand,  seems  to  imply  steps  or  stages  in  thinking  —  a 
passage  of  the  mind  from  one  fact  to  another.  More- 
over, (2)  Inference  differs  from  Judgment  in  exhibiting 
the  grounds  upon  which  its  statement  rests.  The  sim- 
ple judgment  makes  a  declaration  on  the  basis  of  sense- 
perception,  as,  for  example,  'the  mail-train  has  just  gone 
down  ' ;  '  it  rained  yesterday.'  Each  of  these  statements 
stands  alone,  as  it  were  ,  it  does  not  attempt  to  gain 
support  by  pointing  out  the  connection  with  other  facts. 
To  infer,  however,  is  just  to  show  the  necee:sary  con- 
nection of  Tacts  —  that  from  the  presence  or  absence 
of  certain  things,  the  presence  or  absence  of  certain 
other  things  necessarily  follows.  It  is  not  necessary 
for  Inference  that  the  conclusion  reached  should  be  a 
fact  which  was  not  hitherto  known.  We  often  do  reach 
new  truths  by  reasoning  from  necessary  connections. 
Thus  we  might  infer  that  the  mail-train  has  just  gone 
down,  from  the  fact  that  this  train  is  always  on  time, 
and  that  it  is  now  five  minutes  past  the  hour.  Or,  we 
might  prove,  to  a  person  who  doubted  the  correctness  of 
our  memory,  that  it  rained  yesterday,  by  pointing  to 
other  facts  with  which  rain  is  necessarily  connected. 
We  might  point  to  the  muddy  condition  of  the  roads, 
the  swollen  streams,  or,  perhaps,  might  remind  the  per- 
son who  questions  the  statement,  that  it  was  yesterday 
that  A  was  out  driving,  and  came  home  soaking.  In 
this  way,  one  tries  to  exhibit  the  necessity  of  the  fact 
under  consideration  ;  and  to  do  this  is  to  infer. 

In  the  actual  process  of  knowledge,  we  more  fre- 
quently go  from  a  fact  to  its  reasons,  than  in  the  oppo- 
site direction.     The  intelligence  begins  by  accepting  all 


I       I 


1  'i 


!       '  \ 


^m  H'' 


'>    jJi*  ^_mp.--  _j 


* 


iil 


l^^i  11 


■    ! 


li '  - 

i 


lii- 


I 


'           ;| 

320 


Tin:  NATURE  OF   INFERENCE 


the  connections  as  true  and  universal  which  it  meets 
with  in  ordinary  experience,  or  which  are  suggested  to 
it  in  any  way.  It  does  not  trouble  itself  at  all  about 
the  grounds  of  its  judgments,  and  thus  the  insufficient 
basis  on  which  many  of  these  stand  is  at  first  not  evi- 
dent. The  child,  for  example,  believes  everything  which 
it  is  told  by  its  mother  or  nurse,  or  it  may  be,  all  the 
pleasant  things  which  it  imagines.  Very  often,  too,  the 
judgments  of  older  persons  are  determined  by  their  own 
wishes.  The  French  peasant  girl  was  sure  that  it  was 
impossible  for  the  Germans  to  take  Paris.  Another 
principle  upon  which  both  children  and  adults  quite 
unconsciously  proceed,  is  that  the  future  must  always 
resemble  the  past.  The  child  assumes  that  the  order 
of  events  each  day  will  be  the  same,  —  that  there  will 
always  be  games  after  dinner,  and  visitors  in  the  after- 
noon, because  that  has  happened  a  number  of  times  in 
the  past.  And  one  may  have  no  better  reason  for 
believing  that  the  sun  will  rise  to-morrow,  than  the  fact 
that  it  rose  yesterday  and  to-day. 

In  these  early,  unreflective  judgments,  the  ground  or 
principle  upon  which  they  are  based  is,  of  course,  not 
conscious  at  all.  Each  i  udgment  is  accepted  by  itself, 
and  no  questions  are  raised  as  to  iiovv  it  is  known.  But 
the  tlevelopment  of  intelligence  may  be  regarded  as  a 
process  of  becoming  conscious  of  the  reasons  which 
show  the  falsity  of  certain  of  our  beliefs,  and  the  neces- 
sity of  others.  The  original  judgment  is  not  in  reality 
so  isolated  and  unrelated  as  it  appeared  ;  it  contains 
implicitly  its  own  reasons.  But  the  validity  of  its  pro- 
cedure   cannot    be    made    manifest,  until   the   reasons 


§  86.     JUDGMENT   AND   INFERENCE 


321 


11 !      ^ 


ich  it  meets 

suggested  to 

at  all  about 

e  insufificient 

first  not  evi- 

ything  which 

ly  be,  all  the 

iften,  too,  the 

by  their  own 

■e  that  it  was 

s.      Another 

adults  quite 

must  always 

hat  the  order 

lat  there  will 

in  the  after- 

r  of  times  in 

r   reason   for 

than  the  fact 

he  ground  or 
f  course,  not 
ted  by  itself, 
mown.  But 
egarded  as  a 
asons  which 
id  the  neces- 
11  ot  in  reality 
it  contains 
y  of  its  pro- 
the   reasons 


for  the  statement  made  by  the  judgment  are  brought 
to  light.  In  the  development  of  knowledge,  the  judg- 
ment must  expand  so  as  to  show  the  reasons  which  it 
necessarily  presupposes.  In  itself,  it  is  only  a  fragment 
of  the  complete  statement,  and  it  tries  to  complete  itself 
by  making  clear  the  nature  of  the  whole  wliich  it  in- 
volves. It  is  not  until  the  implicit  reasons  which  every 
judgment  contains  are  thus  brought  to  consciousness, 
that  it  can  be  either  provec'  or  disproved.  Taking  the 
mere  judgment  by  itself,  it  is  only  possible  to  place 
one  man's  assertion  against  aT-.other's  denial.  But  proof 
or  disproof  of  a  proposition  implies  that  reasons  are 
given  for  or  against  it.  If  its  connection  with  some 
fact,  or  set  of  facts,  known  to  be  true,  becomes  evident 
on  reflection,  the  fc/t  necessity  which  the  judgment 
possesses  (§  76),  is  transformed  into  logical  necessity. 
But,  if  no  such  connection  can  be  found,  or,  if  the 
judgment  in  question  is  seen  to  presuppose  propositions 
which  are  themselves  false,  we  must,  of  course,  cease  to 
regard  it  as  valid. 

When  a  judgment  develops  so  as  to  become  conscious  of  its 
reasons,  it  has  already  tr^ken  on  the  form  of  Inference.  And,  as 
we  have  ah-eady  seen,  this  is  tlic  usual  procedure  of  knowledj^e. 
We  begin  by  believing  without  reason,  or  we  assume  that  certain 
things  are  true,  and  try  to  find  reasons  for  our  belief.  The  conclu- 
sion, which  is,  of  course,  logically  last,  is  usually  first  for  us,  and  we 
set  out  from  it  to  find  the  grounds,  or  the  premises. 

This  way,  however,  of  proceeding  i^om  conclusion  to 
premises,  or  from  a  judgment  to  its  reasons,  implies 
that  the  mind  is  already  aware  of  the  distinction  be- 
tween false  knowledge  and  true,  and  therefore  that  the 


t- '   <* 


'K     I 


'I  n 


M 


322 


THE  xXATURi:  OF   INFERENCE 


work  of  criticising  and  testing  knowledge  has  already 
begun.  The  criticism  of  knowledge  is  probably  forced 
upon  tiie  mind  at  first  by  the  practical  consequences  of 
false  judgments.  So  long  as  false  judgments  lead  to 
no  unpleasant  results,  they  are  likely  to  pass  unnoticed, 
without  any  question  being  raised  regarding  the  grounds 
by  means  of  which  they  are  supported.  The  child  usu- 
ally believes  all  that  he  is  told,  until  he  discovers  that 
his  credulity  is  making  him  a  laughing-stock,  or  has  led 
to  the  loss  of  some  pleasure  which  he  values.  Sooner 
or  later  he  learns  that  the  ground  upon  which  he  has 
been  unconsciously  proceeding  —  somebody  told  me  — 
is  insufficient.  In  the  same  way,  the  natural  tendency 
to  regard  all  connections  which  we  happen  to  find  ex- 
isting between  events  as  universal  and  necessary,  be- 
comes more  critical  and  discriminating.  The  child  soon 
learns  that  the  events  of  one  day  do  not  necessarily 
follow  in  the  order  of  the  day  before,  and  that  it  is  not 
always  rainy  on  Fridays,  and  fine  on  Sundays.  But,  in 
order  to  discriminate  between  what  is  true  and  what  is 
false,  he  is  obliged  to  go  beyond  the  facts  themselves, 
and  to  become  more  or  less  clearly  aware  of  the  grounds 
assumed  in  each  type  of  judgment.  He  is  forced  to 
include  in  the  judgment  the  reasons  by  which  it  is  sup- 
ported. And,  in  this  way,  the  distinction  between  valid 
and  invalid  principles  of  connection  is  gradually  learned. 
Through  experience,  which  is  more  or  less  dearly 
bought,  we  learn  that  we  cannot  depend  upon  hear- 
say, and  also  that  many  of  the  most  obvious  connec- 
tions between  events  are  not  essential,  and  have  no 
claim  to   be  rejrarded  as  universal   laws.     It  becomes 


1     .  '-h . 


M 


has  already 
bably  forced 
sequences  of 
ents  lead  to 
;s  unnoticed, 
the  grounds 
[le  child  usii- 
iscovers  that 
;k,  or  has  led 
.les.     Sooner 
vhich  he  has 
y  told  me  — 
iral  tendency 
n  to  find  ex- 
ccessary,  bc- 
he  child  soon 
t  necessarily 
that  it  is  not 
lys.      But,  in 
and  what  is 
themselves, 
the  grounds 
is  forced  to 
ich  it  is  sup- 
)ct\veen  valid 
Lially  learned, 
less   dearly 
1  upon  hear- 
ious   connec- 
ind    have    no 
It  becomes 


§80.     JUDGMENT   AND    INILRKNCE 


325 


evident  that  it  is  necessary,  in  order  to  reach  true 
principles  of  connection,  to  take  a  wider  survey  of  the 
facts,  and  to  push  the  process  of  analysis  further  than 
is  done  by  our  orciinary  judgments  of  sense-i)erception. 
For  example,  we  may  at  one  time  have  supposed  it  to 
be  a  universal  law  that  hot  water  will  break  glasses 
when  poured  into  them.  But  as  soon  as  we  have  ex- 
perience of  any  instance  or  instances  to  the  contrary, 
we  see  that  there  is  no  essential  connection  between 
hot  water  and  broken  glasses.  It  is  necessary  then  to 
go  behind  the  obvious  facts  of  tlie  case,  in  order  to  dis- 
cover what  is  the  real  antecedent  in  the  two  cases. 
The  tv*'o  instances  —  where  the  glasses  break,  and  where 
they  do  not — seem  to  be  the  same;  and  yet,  since 
the  result  is  different,  there  must  be  a  difference  which 
further  analysis  will  bring  to  light.  It  is  by  penetrat- 
ing behind  the  point  of  view  of  ordinary  knowledge, 
that  science  endeavours  to  show  how  phenomena  are 
really  and  essentially  connected. 

The  judgments  of  ordinary  adiih  life  usually  involve  some  con- 
sciousness of  their  grounds,  and  are  therefore  so  far  inferences. 
But  in  many  cases  of  this  kind  it  would  be  difficalt  for  the  individual 
to  state  explicitly  the  reasons  for  his  judgment.  The  connection 
which  he  asserts  may  be  guaranteed  to  his  mind  by  some  complex 
set  of  circumstances  very  difficult  to  formulate.  Or  it  may  rest 
upon  some  general  similarity  or  analogy,  which  is  so  obviously  in- 
sufficient that  he  hesitates  to  acknowledge  that  it  is  the  only  ground 
he  has  for  judging.  Thus  one  may  be  vaguely  conscious  that 
one's  only  reason  for  liking  A  is  his  resemblance  to  B.  It  may  be 
impossible  to  say  exactly  in  what  points  A  resembles  B ;  one  may 
proceed  on  a  vague  general  similarity.  Or  one  may  hesitate  to 
make  clear,  even  to  oneself,  that  the  only  reason  for  disliking  A  is 


ail' 


■fl 


1 1 


iY'l 


4in  f 


ijl 


i 


"I 


\- 


J 


324 


THE  NATURE  OF  INFERENCE 


because  of  some  external  resemblance  —  in  name,  or  dress,  or  figure 
—  to  C,  whom  one  dislikes. 

§  87.  The  Nature  of  Inference.  —  Wc  have  seen  that 
it  is  difficult  to  draw  any  hard  and  fast  line  between 
Judgment  and  Inference.  In  general,  however,  we  may 
be  said  to  reason  when  we  do  not  simply  accept  a  fact 
on  the  basis  of  sense-perception  or  meiv  ry,  but  sho;v 
that  it  neces.sarily  follows  from  some  other  known  fact 
or  facts.  Inference,  then,  requires  (i)  that  certain  data 
or  premises  should  be  accepted  as  already  known  ;  and 
(2)  it  implies  an  insight  into  the  necessary  connection 
of  some  new  fact  or  set  of  facts  with  what  we  already 
know.  Thus  one  is  said  to  infer  B,  when  one  sees  that 
it  necessarily  follows  from  some  fact  which  is  already 
known.  It  is  not  necessary  for  an  inference  that  B 
should  never  have  been  in  consciousness  before.  As 
we  have  seen  in  the  last  section,  what  we  very  often  do 
in  inference  is  to  show  the  reasons  or  necessity  of  some 
fact  which  we  have  previously  accepted  without  know- 
ing why.  No  matter  whether  we  go  from  premises  to 
conclusion  (from  the  reasons  to  the  fact),  or  in  the 
opposite  direction,  from  the  conclusion  to  the  premises, 
we  are  said  to  infer  whenever  we  find  the  crround  for 
the  existence  of  one  fact  in  the  nature  of  another  fact. 
In  the  former  case,  we  use  words  like  '  therefore '  and 
'consequently,'  to  indicate  the  connection;  and  when 
the  reasons  are  stated  last,  •  for '  and  *  because.'  When- 
ever these  conjunctions  are  used  correctly,  an  infer- 
ence has  been  made,  and  it  is  always  useful  in  following 
a  course  of  reasoning  to  make  clear  to  ourselves  pre- 
cisely on  what  grounds  it  has  been  made. 


dress,  or  figure 

v^e  seen  that 
ine  between 
;ver,  we  may 
accept  a  fact 
ry,  but  show 
r  known  fact 
certain  data 
known  ;  and 
y  connection 
Lt  we  already 
3ne  sees  that 
:h  is  already 
ence  that   B 
before.     As 
'^ery  often  do 
sity  of  some 
thout  know- 
premises  to 
),   or  in  the 
he  premises, 
ground  for 
another  fiict, 
erefore'  and 
;  and  when 
ise.'     When- 
:Iy,  an   infer- 
in  following 
irselves  prc- 


•,\,N\1 


§87.    THE  NArUkK  OF   INFhRKNCE 


32^ 


Although  Inference  seems  very  simi)le  and  wry 
natural,  its  procedure  is  much  more  puzzling,  when 
looked  at  closely,  than  one  would  at  first  imagine.  As 
we  have  seen,  there  is  no  Inference  unless  the  result 
reached  is  different  from  the  starting-point.  But  how 
are  we  ever  justified  in  passing  from  a  knowledge  of 
one  fact  to  another  different  from  it  .'*  How  can  we 
ever  pass  from  the  known  to  the  unknown  ?  The 
Greeks,  who  loved  to  bring  to  light  the  paradoxes 
which  so  often  underlie  familiar  facts,  used  to  discuss 
this  question.  How  is  it  possible  for  that  which  is 
unknown  —  external  to  the  mind  —  to  pass  into  the 
mind  and  get  itself  known  ?  It  was  to  solve  this  puz- 
zle that  Plato  propounded  the  doctrine  that  all  knowing 
is  remembering.^  Knowledge,  he  declares,  is  not  in- 
creased by  learning  that  of  which  we  were  altogether  '; 
ignorant,  but  by  a  process  of  calling  to  mind  or  recol- 
lecting the  knowledge  which  the  soul  possessed  in  a 
previoi's  state  of  existence,  but  which  was  forgotten 
when  it  entered  upon  the  conditions  of  the  present  life. 
It  was  therefore  no  longer  necessary  to  suppose,  accord- 
ing to  Plato,  that  the  mind  performed  the  impossible 
feat  of  knowing  what  is  external  to  itself,  or  that  things 
previously  unknown  pass  bodily  into  our  minds,  and 
thus  become  known. 

Plato  was  undoubtedly  right  in  protesting  against  the 
popular  view  that  knowledge  is  received  into  the  mind, 
as  food  is  received  into  the  stomach.  Knowledge, 
as   we   have  frequently   seen,  comes  from  within,  not 

^This  is  the  theory  upon  which  Wordsworth  bases  his  "Ode  on  the 
Intimations  of  ImmortaUty." 


'1 


4      ' 


i        \' 


1 


m^ 


326 


THE   XAILKI-:   OF   INKERLNCE 


from  without.  lUit  the  apparent  paradox  of  knowledge 
may  be  exphiiiied  without  adopting  Plato's  jioetical 
notion  of  a  previous  state  of  existence.  We  may  admit 
that  the  process  of  inference  would  be  quite  inex- 
plicable, if  it  proceeded  from  one  fact,  A,  to  a  know- 
ledge of  a  second  fact,  H,  which  is  totally  different  from 
the  former.  When  we  examine  cases  of  inference,  how- 
ever, we  find  that  there  is  always  a  certain  amount  of 
identity  between  the  two  ends  of  the  process.  The  con- 
clusion is  always  different,  and  yet  not  entirely  different 
from  the  premi'^cs.  Thus,  from  the  propositions,  '  all 
metals  nre  elementary  substances,'  and  '  gold  is  a  metal,' 
one  can  infer  that  gokl  is  an  elementary  substance. 
It  is  possible  to  connect  '  gold  '  and  '  elementary.'  Here 
the  identical  link --what  is  called  in  formal  logic  the 
middle  term  — is  'metal.'  It  is  possible  to  connect  gold 
and  elementary  substance,  because  the  former  is  at  the 
same  time  a  metal,  which  in  its  turn  is  an  element.  Of 
course,  these  conceptions  —  gold,  metal,  element  —  are 
not  absolutely  indentical  ;  it  was  pointed  out  in  (§  79) 
that  prepositions  cannot  be  regarded  as  expressing 
mere  identity  without  difference.  But  we  can  say  that 
there  is  a  common  thread  or  element  running  through 
these  notions,  which  furnishes  the  principle  of  con- 
nection. Where  we  cannot  discover  such  a  common 
nature,  no  inference  can  be  made.  Thus,  for  example, 
it  would  be  impossible  to  draw  a^ty  conclu.-" m  from 
the  statements  that  '  it  rained  yesterday  '  and  '  gold  has 
been  discovered  in  Alaska,'  because  there  is  no  com- 
mon eljiiient  or  connecting  tliread  present  wh'ch  would 
lead  us  beyond  the  premises. 


\ 


^- 


§  87.    riiK  NA ruKK  01   inii:ri:nce 


127 


knowlccl<;e 
[)'s  ])()ctical 
;  may  admit 
quite  inex- 
to  a  knovv- 
ffcrcnt  from 
^rcnce,  how- 
i  amount  of 
5.  The  con- 
ely  different 
ositions,  '  all 
1  is  a  metal,' 
'•  substance, 
tary.'  Here 
al  logic  the 
:onnect  gold 
ler  is  at  the 
ement.  Of 
nncnt  —  are 
ut  in  (§79) 

expressing 
an  say  that 
ing  through 
3le    of    con- 

a  common 
[)r  example, 
lu.~'  )n  from 
1  '  gold  has 

is   no   com- 
ivhich  would 


In  formal  arguments  the  mitUlle  term,  or  connectin^j  link,  is  usu- 
ally explicitly  stated  ;  but  in  the  actual  process  of  reasor)in«:  tilings 
out,  it  is  frecjuently  necessary  to  go  in  search  of  it.  We  n-i;<y  notice, 
for  example,  that  the  tire  in  a  stove  burns  more  slowly  \vh*n  the 
damper  is  shut.  In  order  to  understand  the  fact,  we  have  to  find  out 
some  fact  which  is  common  to  •  closed-dam  p  j  r "  and  'slow-burning,' 
some  link  of  identity,  as  it  were,  wliich  enables  us  to  pa.ss  from  \\\v 
one  to  the  other.  Such  a  connecting  link  is  afforded,  of  course,  in 
this  case  by  the  supply  of  oxygen.  Darwin  was  noted  for  his  keen- 
ness in  detecting  connections  wliich  escajjed  tlie  ordinary  eye.  as 
well  as  for  his  skill  in  giving  explanations  of  tlieni.  On  one  occa- 
sion, he  observed  that  in  the  part  of  the  country  whero  he  lived, 
clover  was  abundant  in  those  fields  which  were  situated  near  viUages, 
while  the  outlying  fields  were  almost  destitute  of  it.  What  now,  lie 
asked  himself,  is  the  connecting  link  between  these  facts?  Some 
investigation  of  the  matter  convinced  him  that  the  two  agencies 
which  produced  this  result  were  mice  and  cats.  The  field  mice 
destroy  the  clover  by  feeding  upon  its  roots,  but  the  cats  go  out  from 
the  villages  into  the  fields  near  by  and  kill  the  mice. 

We  have  seen  that  the  passage  frotn  one  fact  to  an- 
other in  inference  does  not  involve  a  transition  to  some- 
thing wholly  different  from  the  starting-point.  There  is 
always  some  aspect  or  feature  in  which  the  premises  are 
identical  with  the  conclusion.  And  it  is  on  the  strength 
of  this  identity  that  a  passage  can  be  tnade  from  one  to 
the  other.  The  same  fact  may  be  expressed  differently 
by  saying  that  all  inference  takes  place  within  a  system, 
*  where  the  parts  are  so  held  together  by  a  common 
nature  that  you  can  judge  from  some  of  them  what  the 
nature  of  the  others  must  be.'  Suppose  you  were  given 
the  leaf  of  a  plant.  If  you  had  some  sy.stematic  botani- 
cal knowledge,  it  would  be  possible  to  infer  the  species 
of  plant  to  which   the   leaf  belonged.      That  is,  from 


I  I 


'* 


■«,: 


fr' 


.1  'II 


'if 


hi 

I 
I 


I 


::«i 


■ 

( 

K 

r 

i 

"ft' 

t     1 

El 

kl 

328 


ill  I-:  NATURE  OF   IM-EKEXCE 


the  nature  of  a  part,  the  nature  of  the  whole  to  which  it 
belongs  con^  '  'ic  determined.  The  part  represents  the 
whole  —  in  some  sense  contains  it  implicity.  It  is  said 
that  the  great  naturalist  Cuvier  could  determine  by  ex- 
amining a  single  tooth  the  nature  of  the  animal  to  which 
it  belonged.  Let  us  sui)pose  that  the  tooth  were  that  of 
a  ruminant  animal.  Now  a  zoologist,  who  knows  the 
characteristics  of  such  an  animal,  could  draw  various  in- 
ferences regarding  the  possessor  of  the  tooth.  He  could 
conclude,  for  example,  that  the  animal  to  which  it  once 
belonged  must  also  have  had  cloven  hoofs.  A  single 
piece  or  part,  that  is,  would  enable  one  who  knows  the 
system  or  common  nature  to  which  all  the  parts  be- 
long, to  judge  what  the  other  parts  are  like. 

The  exami)les  just  given  have  referred  to  the  possi- 
bility of  an  inference  of  one  part  of  an  organism  to 
another.  But,  as  we  '^ive  already  seen,  the  systematic 
connection  which  here  exists  between  the  parts,  is  more 
or  less  completely  present  whenever  it  is  possible  to 
infer  at  all.  Inference  pushes  further  the  work  of  con- 
structing a  system  begun  by  Judgment  (§78).  If  each 
thing  was  known  by  itself,  if  the  parts  of  our  knowledge 
did  not  fall  together  into  systems  where  each  part  to 
some  extent  determines  the  nature  of  the  other  parts,  no 
inference  would  be  jiossible.  It  is  because  the  various 
pieces  of  our  knowledge  are  never  independent  of  each 
other,  but  form  an  organic  whole,  like  the  members  of  a 
living  organism,  that  certain  facts  follow,  as  we  say, 
from  certain  other  facts.  And  it  is  of  course  true,  that 
as  our  knowledge  in  any  field  becomes  more  completely 
organized,  it  is  more  possible  to  use  it  as  a  basis  for  in- 


§88.     IXDlcriOX    AND    DKDrCIIOX 


329 


Ic  to  which  it 
^presents  the 
I.  It  is  said 
rminc  by  cx- 
mal  to  which 
were  that  of 
)  knows  the 
.w  various  in- 
h.  He  could 
^hich  it  once 
s.  A  sin<;le 
o  knows  the 
he  parts  be- 

to  the  possi- 
organism  to 
c  systematic 
arts,  is  more 

possible  to 
A'ork  of  con- 
8).  If  each 
r  knowledge 
ach  part  to 
ler  parts,  no 

the  various 

ent  of  each 
embers  of  a 

as  we  say, 
se  true,  that 

completely 
)asis  for  in- 


ference. The  better  we  are  able  to  put  together  in  a 
systematic  way  the  various  facts  which  we  have  learned 
about  geology,  or  astronomy,  or  the  weather,  the  more 
sii^nificant  each  fact  becomes.  The  geologist  may  be 
able  to  tell  from  the  appearance  of  the  cliffs  what  has 
taken  place  in  a  locality  thousands  of  years  ago.  And, 
similarly,  for  the  fisherman,  the  temperature,  direction 
of  the  wind,  its  rising  or  falling,  etc,  are  all  sii^iis  from 
which  he  is  able  to  infer,  more  or  less  correctly,  the 
kind  of  weather  which  may  be  expected.  A  person 
who  had  no  systematic  knowledge  in  either  of  these 
fields,  would,  however,  see  nothing  in  the  scarred  rocks, 
or  in  the  sudden  change  of  the  wind ;  he  might  notice 
the  facts,  but  would  not  be  able  to  use  them  as  a  basis  of 
inference. 

It  is  important  to  notice  that  what  has  just  been  said  ^ocs  to 
confirm  our  previous  statements  regarding  the  increasing  degree  of 
integration  wliich  knowledge  shows  in  the  course  of  its  development. 
The  knowledge  of  die  scientist  ditTers  from  that  of  the  ordinary  man, 
not  only  in  the  greater  number  of  facts  which  the  latter  contains,  but 
also,  as  we  have  seen,  in  the  degree  of  integration  or  coherence 
which  these  facts  possess.  Inference,  then,  is  simply  a  deep  insight, 
based  on  definite  knowledge,  into  the  necessary  connection  of  things. 
It  is  an  act  of  thought  which  discovers  the  essential  relations  be- 
tween things  which  at  first  sight  appear  to  have  no  connection  with 
each  other.  As  has  already  been  said,  it  is  a  reasoned  judgment ; 
I.e.,  a  judgment  which  has  become  conscious  of  the  reasons  for  the 
connections  which  it  affirms. 

§  88.  Induction  and  Deduction.  —  It  has  been  already 
pointed  out  that  there  are  two  directions  in  which  infer- 
ence or  reasoning  may  proceed.  We  may  begin  with 
certain  facts  or   principles  which    arc  already  known, 


IM 


y 


'H 


i.  " 


r 

1     : 

i, 

.'i'      ill 

If 


i  i 


'   ^ 


330 


TIIK   NATUKK   Ul    INI  EKKXCE 


or  arc  assumed  to  be  true,  and  i)roceed  to  show  that 
some  result  uecessarily  loUows  from  them.  Thus  we 
might  infer  thai  if  the  draughts  of  a  stove  are  closed  so 
that  the  supply  of  oxygen  is  lessened,  the  fire  will  burn 
slowly  ;  or  from  the  relative  positions  and  revolutions  of 
the  planets,  that  an  eclipse  of  the  sun  will  take  place  on 
a  specified  day  and  hour.  This  method  of  reasoning  is 
known  as  Deduction.  It  j)roceeds,  as  we  have  seen, 
from  premises  to  conclusion.  In  the  first  part  of  this 
book,  this  form  of  reasoning  has  been  treated  at  some 
length  and  its  rules  of  procedure  stated.  At  present, 
\vc  need  only  notice  that  in  deductive  reasoning  the  par- 
ticular case  is  always  brought  under  some  general  law 
or  principle,  which  is  already  known  or  assumed  as  true. 
Socrates  is  known  to  be  mortal,  because  as  a  man  he 
falls  under  the  general  law  that  all  men  are  mortal ;  the 
closing  of  the  draughts  is  a  case  of  lessened  supply  of 
oxygen,  and,  therefore,  in  accordance  with  the  general 
law,  a  case  of  slow  burning.  A  deductive  inference 
shows  what  are  the  results  of  the  application  of  a  gen- 
eral law  to  particular  facts  or  instances.  It  proceeds 
downwards,  as  it  were,  from  the  general  law  to  its  con- 
sequences. 

In  Induction,  on  the  contrary,  the  procedure  is  just 
the  opposite  of  this.  We  begin  with  particular 
phenomena,  and  try  to  discover  from  them  the  law 
or  principle  which  unites  them.  Certain  facts  are 
observed  to  happen  together,  and  the  problem  is  to 
find  the  ground  or  explanation  of  this  connection. 
Inductive  inference  is  thus  a  process  of  reading  the 
general  law  out  of  the  particular  facts.     It  is  an  insight 


§  SS.     INDUCTION    AND    Dl'-DUCITUN 


331 


show  that 
Thus  vvc 
c  closed  so 
c  will  burn 
evolutions  of 
kc  place  on 
easoning  is 
have  seen, 
Ydi't  of  this 
;cd  at  sonic 
\t  present, 
ing  the  par- 
,^eneral  law 
ncd  as  true, 
i  a  man  he 
mortal ;  the 
:1  supply  of 
he  general 
z  inference 
1  of  a  gen- 
t  proceeds 
to  its  con- 
lure  is  just 
particular 
Ini  the   law 
facts   are 
)lem   is  to 
:onnection. 
jading   the 
an  insight 


into  the  nature  of  the  whole  or  system,  based  upon  a 
careful  examination  of  the  parts.  •  Yesterday  the  smoke 
tended  to  fall  to  the  ground,  and  it  rained  in  the  after- 
noon.' These  two  facts  may  simply  be  observed  a 
number  of  times  without  any  tlunight  of  their  con- 
nection. lUit  intelligence  asks :  Why  should  they 
happen  in  conjunction  ?  And  to  answer  this  cpiestion, 
vvc  must  begin  by  analyzing  the  facts  in  our  possession. 
When  the  smoke  falls  to  the  ground,  the  atmosphere 
must  be  heavier  than  usual ;  this  is  the  case  when  it 
contains  a  great  deal  of  moisture ;  but  when  the 
atmosphere  is  in  this  condition,  it  usually  tends  to 
discharge  its  moisture  in  the  form  of  rain  ;  therefore 
we  have  the  general  law  which  enables  us  to  show  that 
the  behaviour  of  the  smoke  and  the  rain  yesterday  were 
not  only  accidentally  conjoined,  but  essentially  connected. 
Deduction  and  Induction,  then,  are  both  forms  of 
inference,  but  the  starting-point  and  mode  of  procedure 
of  the  one  is  different  from  that  of  the  other.  Conse- 
quently, it  is  not  unusual  to  speak  of  them  as  two  ki)ids 
of  reasoning  which  are  quite  distinct  and  independent 
of  each  other.  It  is,  however,  important  to  avoid  this 
popular  error,  and  to  remember  that  the  real  process  of 
inference  is  in  each  case  the  same.  The  essence  of 
inference,  as  has  been  shown,  consists  in  the  fact  that 
it  exhibits  the  manner  in  which  particular  facts  are 
connected  together  into  a  system  or  whole.  And  this 
end  is  achieved  both  by  Deduction  and  Induction.  In 
the  former  case,  the  general  law  of  connection  —  what 
we  may  call  the  nature  of  the  system  within  which  the 
particulars  fall  —  is  known,  and  we  argue  from  this  as 


Xi\ 


y 

I': 
1 , 


'^ij; 


>  I 


332 


THE  NATURE  Or   INFERENCE 


;  \ 


^ '  1 

■' 

^ 

i 

:         ' 

H 

< 

1 

i 

'Mm' 

m 

( 

f 

i 

*■* 

. 

4w 
4IP 

k 

to  the  nature  and  relations  of  the  various  parts  which 
fall  within  it.  We  have  the  common  thread  which 
unites  the\arious  facts  in  our  hand,  and  following  it  out 
are  able  to  show  its  application  in  determining  the 
nature  of  events  which  have  not  yet  come  within  the 
range  of  our  experience.  Knowing  the  law  of  gravity, 
for  example,  one  could  infer  deductively  what  momentum 
a  ball  weighing  one  pound  must  necessarily  have  after 
falling  one  hundred  feet.  It  would  not  be  necessary 
actually  to  measure  the  momentum  of  the  falling  body 
in  this  particular  case,  but  it  could  be  shown  to  be  the 
necessary  result  of  the  general  law.  What  the  deductive 
inference  shows  to  us,  is  the  way  in  which  a  general 
principle  or  law  of  connection  runs  through  a  group  of 
facts,  and  cor  titutes  them  a  real  or  organic  whole. 
The  same  insight  is  reached  by  inductive  inference, 
although  the  starting-point  is  entirely  different.  As 
we  have  already  seen,  induction  begins  by  observing 
that  certain  phenomena  are  frequently  conjoined,  and 
attempts  to  discover  some  law  or  principle  which  will 
make  che  fact  of  their  connection  intelligible. 

It  is  usual  to  say  that  in  induction  we  go  from  the 
particular  facts  to  the  general  law.  The  following,  how- 
ever, would  be  a  more  correct  form  of  statement  : 
Before  the  inference,  we  observe  that  a  number  of  phe- 
nomena occur  togeth  _r,  but  do  not  know  whether  this 
conjunction  is  necessary  or  not ;  or,  if  we  assume  that 
it  is  necessary,  we  do  not  understand  why  it  should  be 
so.  As  a  result  of  the  inductive  inference,  we  gain  an 
insight  into  the  necessary  connection  of  the  observed 
phenomena,  and  also  understand  the  principle  according 


I 


§88.     INDUCriON   AND   DEDUCTION 


333 


!1?     ' 


parts  which 
read   which 
owing  it  out 
•mining  the 
;  witliin  the 
'•  of  gravity, 
;  momenLum 
y  have  after 
!e  necessary 
falHng  hody 
,vn  to  he  the 
he  deductive 
h  a  general 
;h  a  group  of 
janic  whole, 
e   inference, 
fforent.     As 
)y  observing 
njoined,  and 
e  which  will 
le. 

I  go  from  tlie 
[lowing,  how- 
statement  : 

Inber  of  })he- 
Ivhether  this 
[assume  that 

lit  should  be 
we  gain  an 

llie  observed 

lie  accorchng 


to  which  the  latter  are  united.  What  we  really  obtain 
through  an  inductive  inference  is  not  only  a  general  law, 
but  also  a  perception  of  its  concrete  application  to 
particular  phenomena.  This  being  so,  it  is  clear  that 
Induction  and  Deduction  are  not  two  different  kinds  of 
inference.  Inference  always  implies  an  effort  on  tlie 
pr.'"t  of  the  mind  to  see  how  phenomena  are  neces- 
sarily connected  according  to  some  general  })rinciple. 
And,  in  carrying  out  this  purpose,  the  mind  must  begin 
with  the  knowledge  which  it  already  possesses.  When 
the  general  law  of  connection  is  known,  and  the  object 
is  to  discover  the  nature  of  some  particular  fact,  the  / 
method  of  procedure  is  deductive.  But,  when  the 
problem  by  which  we  are  confronted  is  to  read  out  of 
the  facts  of  sense-perception  the  general  law  of  their 
connection,  the  method  of  inference  which  must  be 
employed  is  that  of  inducticjn.  lUit  from  whatever 
point  we  set  out,  and  whatever  may  ])e  the  inmiediate 
object  of  the  inference,  the  result  is  always  the  same  — 
an  insight  into  tlie  necessary  connection  of  facts  accord- 
ing to  some  general  principle. 

It  is  not  unusual  to  hear  the  remark  made  that 
modern  science  has  been  built  up  by  the  employment 
of  the  inductive  method.  This  must  not,  however,  be 
interpreted  to  mean  that  deductive  inferences  are  not 
also  used  in  the  discovery  of  scientific  truth.  Science 
(which  is  simply  another  name  for  systematic  know- 
ledge) is  the  product  of  thinking,  and  thought,  as  we 
have  seen,  is  not  limited  to  any  one  mode  of  procedure. 
Thought  aims  at  extending  knowledge,  and  so  long  as 
it  can  find  any  link  of  connection,  or  guiding  thread,  it 


.i; 


f 


334 


THE   NATURE   UE    IXEEKEXCE 


:   i 


] 

1'    '^' 

1 

li 

f^K '  '■ 

i  1 


i 


%* 


is  not  limited  to  any  one  direction,  or  to  any  fixed  mode 
of  working.  It  is,  of  course,  to  be  admitted  —  and 
this  is  vvliat  is  true  in  the  statement  wiiich  we  have 
quoted  —  that  general  laws  cannot  be  discovered  with- 
out an  examination  of  particular  facts,  and  that  their 
validity  must  always  be  tested  by  comparison  with  the 
facts.  But  as  soon  as  a  general  law  is  discovered  in 
any  field,  it  is  always  used  as  a  principle  from  which  to 
deduce  new  results.  When  it  is  possible  to  employ 
mathematics  in  the  calculation  of  these  results,  it  is 
usually  possible  to  extend  our  knowledge  of  the  subject 
much  more  rapidly  than  before.  Thus  physics  and 
astronomy  owe  their  rapid  development  to  the  applica- 
tion of  mathematics.  It  must  be  rememberetl,  however, 
that  this  presupposes  a  certain  stage  of  advancement  — 
a  certain  inductive  stage,  as  it  were  —  on  the  part  of 
the  science.  But  even  in  this  earlier  stage,  we  are 
constantly  employing  deduction, — reasoning  out  the 
results  of  certain  guesses  or  suggestions  to  see  if  they 
hold  true  (cf.  §  47).  ]?oth  in  ordinary  life,  and  in 
scientific  procedure,  we  may  see,  Induction  and  Deduc- 
tion are  constantly  employed  together. 

References 

B.  Bosanquct,  Lot^/c,  Vol.  II.  Cii.  I. 

F.  H.  Bradley,  '/'/it'  l^ri  tut  pics  of  Loi^ic,  pp.  430-46S, 

W.  James.  'J7tc  rrinciplcs  of  Psyclioloi^y.  Vol.  II.  Ch.  XXII. 

J.  G.  Hibben,  Induct ivc  Loj^ic,  Chs.  I.  and  II. 


\f  fixed  mode 
nitted  —  and 
ich  wc  have 
ovcrcd  with- 
id  that  their 
son  with  the 
liscovered  in 
•om  which  to 
e  to  employ 
results,  it  is 
f  the  subject 

physics  and 
)  the  applica- 
:red,  however, 
vancement  — 
11  the  part  of 
itage,   we  are 

ing   out    the 
o  see  if  they 

life,    and  in 
and  Deduc- 


Ch.  XXII. 


CHAPTER   XXV 

RATIONAL    AND    EMPIRICAL    THEORIES 

§  89.  The  Point  of  View  of  Rationalism.  —  In  the  his- 
torical sketch  of  logic  given  in  Chapter  II.,  it  was  stated 
that  there  are  two  rival  accounts  of  the  nature  of  know- 
ledge, and  the  methods  by  which  it  is  attained  (cf.  §  8). 
The  first  of  these  theories  is  known  as  Rationalism,  and 
has  its  best  known  historical  representative  in  Descartes; 
while  Empiricism,  the  opposing  theory,  is  associated  with 
the  names  of  the  great  thinkers.  Bacon  and  Locke. 
The  doctrines  of  both  these  schools  have  been  fre- 
quently modified,  and  the  contrast  between  them  is 
now  no  longer  so  pronounced  as  it  was  formerly.  In 
spite  of  this  fact,  however,  the  division  has  always 
represented  two  schools  of  thought  whose  general  re- 
lations to  each  other  have  remained  comparatively  con- 
stant. In  general,  too,  it  has  been  true  that  English 
thinkers  have  upheld  ICmpiricism,  while  Rationalism 
has  hr^d  its  home  on  the  Continent  —  at  first  in  Erance, 
and  later  in  Holland  and  Germany. 

Rationalism  regards  mathematics  as  the  type  of  all 
knowledge.  Its  essential  characteristic  consists  in  the 
fact  that  it  undertakes  to  derive  all  knowledge  from 
general  principles.  These  principles  have  sometimes 
been  regarded  as  innate  (truths  which  are  stamped 
upon  the  mind  at  birth),  or  it  has  been  supposed  that 

335 


'tn 


i,V 


:M 


iHi 


I'll 


U 


<ii 


B 

fi 

K 

•1 

'!■ 

33^^ 


RATIONAL   AND    KMPIRICAl,    rilKOKIKlJ 


they  arc  in  some  way  known  ])ef()rc  experience,  and 
have  a  riL;ht  to  the  title  of  a  priori  i)roi)ositions  (§  76). 
NotwithstandiniT  the  various  forms  in  which  their  thco- 
rics  have  been  expressed,  all  rationalistic  thinkers  agree 
in  regarding  the  first  principles  upon  which  our  know- 
ledge is  based,  as  upon  a  different  plane  from  the  facts 
of  ordinary  life.  While  the  latter  arc  known  only  by 
experience,  and  may  be  wholly  or  partially  false,  the 
former  are  described  as  principles  which  are  in  them- 
selves necessary,  truths  the  opposite  of  which  is  incon- 
ceivable, or  sometimes  as  the  axioms  presupposed  in  all 
experience.  These  principle  s  being  accepted,  the  prob- 
lem which  lay  before  Rationalism  was  to  shov/  how  all 
the  facts  of  our  experience  necessarily  follow  from 
them,  just  as  the  various  propositions  of  geometry 
follow  from  the  definitions  and  axioms  which  are  as- 
sumed as  the  starting-point.  As  a  matter  of  fact,  l:ow- 
ever,  the  famous  Jewish  thinker,  Spinoza  (1632-1677), 
was  the  only  man  who  ever  attempted  to  carry  out 
Rationalism  in  this  systematic  form.  In  general,  one 
may  s?.y  that  rationalistic  thinkers  have  been  mainly 
interested  to  show  that  the  facts  of  the  moral  and  reli- 
gious experience  are  logically  derivable  from  certain 
necessary  first  principles.  It  was  questions  like  those 
regarding  the  existence  of  God,  the  immortality  of  the 
soul,  and  the  freedom  of  the  will,  which  the  rationalists 
were  an.vious  to  put  beyond  disi:)Ute.  And,  as  a  con- 
sequence, not  nearly  the  same  amount  of  effort  was 
devoted  to  showing  how  the  other  facts  of  exjieriencc 
could  be  similarly  derived  from  general  principles. 
It  will  be  at  once  clear,  from  what  has  been  already 


IKS 


§90.      rilK   DOCTRINK   OF   KMriRICISM 


337 


icrioncc,  and 
itions  (§   76). 
h  their  thco- 
linkcrs  agree 
h  our  know- 
rom  the  facts 
own  only  by 
lly  false,  the 
are  in  them- 
hich  is  incon- 
ipposcd  in  all 
ted,  the  prob- 
show  how  all 
follow   from 
of    geometry 
.vhich  are  as- 
of  fact,  how- 
(1632-1677), 
to  carry  out 
general,  one 
been  mainly 
loral  and  reli- 
from   certain 
ns  like  those 
rtality  of  the 
e  rationalists 
id,  as  a  con- 
)f   effort  was 
)f  exjicriencc 
nciples. 
been  already 


said,  that  the  great  instrument  of  knowledge  from  this 
standpoint  must  be  reason.  Very  little  attention  is  paid 
to  perception,  and  the  experience  which  it  furnishes  is 
not  regarded  as  entitled  to  the  name  of  knowledge. 
In  order  to  know,  in  the  true  sense  of  the  word,  it  is 


•tH 


necessary  to  show  the  systematic  connection  of  every 
fact  with  some  fundamental  first  princii)le ;  and  this, 
of  course,  can  be  done  only  by  the  emiiloyment  of 
reasoning.  Perception  gives  us  only  the  bare  facts  ;  it 
is  reason  which  enables  us  to  trace  the  mutual  connec- 
tions, and  derivation  of  these  facts  from  some  general 
law.  The  weakness  of  the  rationalistic  position  does  not 
coiisist  in  its  insistence  on  the  necessity  of  connecting 
the  particular  facts  of  experience  with  general  laws  or 
princii)les,  but  in  the  assumption  upon  which  it  ])ro- 
ceeded  that  these  principles  could  themselves  be  derived 
from  some  other  source  than  experience.  The  result 
was  that  the  rationalists  employed  themselves  t(K)  ex- 
clusively in  deducing  facts  from  general  jirojiositions 
which  were  assumed  to  be  true  without  sufficient  criti- 
cism and  examination.  They  saw  clearly  enough  that 
mere  perception  without  general  principles  can  never 
give  us  knowledge,  but  they  did  not  understand  that  it 
is  impossible  to  separate  the  latter  from  the  former, 
and  to  regard  principles  as  existing  in  the  mind  prior 
to  experience. 

§  90.    The  Doctrine  of  Empiricism.  —  Empiricism  main- 
tains that  all  knowledge  is  derived  from  experience  ,  and 
by  experience  is  understood  the  separate  unconnected 
facts  with  which  the  mind  is  furnished  in  perception. 
z 


!,^ 


'Um 


^f^ 


i 


Fi  ti 


I     ^\ 


'U  fi 


I  ;  i'^ 


^■| 


i^ 

1 

11'^ 

h          E 

^- 

if' 

Hv 

■          ' 

fcji 

* 

K 

5 

K 

.i 

K 

1 

■i 

,i 

1' ' 

m    ■ 

1 

m  ■' 

1' 

a     ' 

r 

'  ^iill 

k 

I     'r*^ 

^ 

««i^  no  ' 

33^ 


KATKXXAL   AND    K.Ml'IKICAL    1  lIKoRItS 


Empiricism  refuses  to  admit  that  we  possess  any 
store  of  first  ])riiiciples  or  general  truths  which  arc 
native  to  the  mind,  or  are  ol)tained  fnnn  any  other 
source  than  experience.  It  is  impossil)le  for  the  mind 
to  know  anythin<;  of  which  it  has  iiad  no  perception. 
Moreover,  the  very  fact  that  perception  is  made  the 
standard  of  knowledi^e,  led  to  the  belief  that  the  mind 
is  somethin<;  essentially  passive,  upon  which  ideas  are 
impressed  by  external  forces.  ICmpiricisni  regards 
knowledge  as  the  sum  of  the  particular  facts  furnished 
to  the  mind  through  sense,  not  as  a  system  which  is 
the  product  of  the  mind's  own  activity.  As  a  conse- 
quence, there  results  an  entirely  different  theory  of 
knowledge  from  that  which  we  have  given  in  this  brxik. 
Ideas  are  supposed  to  be  furnished  to  the  mind  by 
the  channel  of  the  senses,  or  are  compounded  from 
simpler  elements  which  are  supplied  in  this  way.  And 
when  ideas  become  united  by  standing  in  juxtaposition, 
or  being  associated  in  some  other  way,  the  result  is  a 
judgment.  In  this  account,  the  judging,  or  interpreting 
activity  of  the  mind,  which  we  have  made  the  source 
of  all  knowledge,  is  wholly  omitted.  Indeed,  one  may 
say  that  empirical  theories  undertake  to  explain  know- 
ledge without  reference  to  the  mind  and  its  mode  of 
activity.  Although  all  emjjirical  thinkers  do  not  deny 
the  existence  of  the  mind,  yet  none  of  them  wish  to  go 
beyond  the  particular  facts,  and  to  call  in  its  aid  as  d 
principle  of  explanation. 

The  same  insistence  upon  particular  facts,  and 
avoidance  of  general  principles,  is  characteristic  of 
empirical  theories   of  reasoning.      All    inference,  it  is 


IKS 

possess  any 
s  which  arc 
1  any  other 
for  the  mind 
1  perception. 
is  made  the 
hat  the  mind 
ich  ideas  arc 
:ism  re;;ards 
cts  furnished 
item  which  is 

As  a  consc- 
:nt  theor\'  of 
\  in  this  b<rK>k. 
the  mind  by 
oundcd  from 
is  way.  And 
juxtaposition, 

c  result  is  a 
|r  interpreting 
lie  the  source 
|ecd,  one  may 

\j)lain  know- 
its  mode  of 
do  not  deny 

m  wish  to  go 
its  aid  as  a 

r    facts,  and 

Iracteristie    of 

tcrence,  it  is 


§  .JO.   tiil:  doctkim-:  of  lmi'Iricis.m 


339 


maintained,  is  based  upon  a  perception  of  r>'scm 
blance  between  individual  cases.  The  general  law, 
or  principle,  is  nothing  in  itself  but  an  abbreviated 
statement  of  the  manner  in  which  all  the  instances 
act  which  we  have  hitherto  observed.  The  clearest 
statement  of  this  theory  is  given  by  John  Stuart 
Mill,  from  whose  work  on  Loi^ic  the  following  i)as- 
sages  are  taken:  "Now,  all  which  man  can  observe 
are  individual  cases.  From  these  all  general  truths 
must  be  drawn,  and  into  these  they  may  again  be 
resolved  ;  for  a  general  truth  is  but  an  aggregate  of 
particular  truths,  a  comprehensive  exjiression  by  means 
of  which  an  indefinite  number  of  individual  facts  iire 
affirmed  or  denied  at  once.  .  .  .  From  instances  which 
we  have  observed,  we  feel  warranted  in  coiicliicling  that 
what  we  found  true  in  those  instances  holds  in  all  simi- 
lar ones,  j)ast,  j)resent.  and  future,  however  numerous 
they  may  be.  .  .  .  When,  therefore,  we  conclude  from 
the  death  of  John  and  Thf)mas,  and  every  other  j)erson 
we  ever  heard  of  in  whose  case  the  experiment  had 
been  fairly  tried,  that  the  Duke  of  Wellington  is  mortal 
like  the  rest,  we  may  indeed  pass  through  the  generali- 
zation. All  men  are  mortal,  as  an  intermediate  stage  ; 
but  it  is  not  in  the  latter  half  of  the  process,  the  descent 
from  all  men  to  the  Duke  of  Wellington,  that  the  inft-r- 
oicc  resides.  The  inference  is  finished  when  we  have 
asserted  that  all  men  arc  mortal.  What  remains  to  be 
performed  afterwards  is  merely  decij:)hering  our  own 
notes."  ^  In  other  words,  Mill  maintains  that  all  in- 
ference  is    based    upon    the    perception   of    ])articular 

1  Mill,  Logic,  lik.  11.  Ch.  III.  §  3. 


340 


RATIONAL   AND   KMPIKICAL  TIIKOKIKS 


!   1^1 


lifi 


r.j  f 

■  / 

'if 


r-l 


I 

■     r   : 

i«    ' 

ii'l 

cases.  There  is  no  such  n  thi'n<^  as  reasonini;  from 
general  truths  or  |)rip,cii)les.  We  may,  indeed,  arrive 
at  such  ^^eneral  truths  l)y  rejjealed  experiences,  and 
store  them  up  as  maxims  in  our  memory  ;  but  they  [u-e 
not  at  all  necessary  for  the  process  of  inference,  which 
may  be  said  to  be  always  inductive  in  character,  since 
it  sets  out  from  a  perception  of  individual  cases.  "In- 
duction, projierly  so  called,  .  .  .  may  be  defined  as  a 
L;enerali/ati()n  ♦rem  experience.  It  consists  in  i.-.Tcrriiig 
from  s  a:0  '  ivivlual  iv'stancus  in  which  a  phenome- 
non is  ol>;-.eu'ed  to  occur,  that  it  occurs  in  all  instances 
of  a  certui  cia,  ■  namely,  in  all  which  rcsc})iblc  the 
former  in  what  are  regarded  as  the  material  circum- 
stances." 1 

This  account  of  the  way  in  which  inference  proceeds 
undoubtedly  contains  much  that  is  true.  Nevertheless, 
it  is  not,  I  think,  an  adequate  statement  of  the  nature  oi 
inference.  What  one  misses  chiefly  is  some  insistence 
upon  the  fact  that  it  is  only  in  virtue  of  some  identical 
link,  or  common  element,  which  is  present  in  all  the 
individual  cases,  that  one  is  able  to  [)ass  from  one  to 
another.  On  this  point  we  must  refer  to  what  was  said 
in  the  last  chapter  (§  ^j).  It  will  perhaps  be  po.ssible 
to  gain  a  clearer  idea  of  what  is  true  and  what  is  false 
in  this  theory,  by  considering  further  Mill's  doctrine, 
that  it  is  possible  to  reason  from  one  particular  fact  to 
another,  without  any  reference  to  general  truths. 

§  91.  Reasoning  from  Particulars  to  Particulars.  —  *•  Not 
only  may  we  reason  from  particulars  to  particulars,  with- 

1  iMiU,  /.,-i-7V,  15k.  III.  Ch.  111.  §  I. 


IKS 


§91.     FROM    PARTICULARS  To    rAR'lK  l'I,ARS        34I 


^onini;  from 
idced,  arrive 
ricncos,  and 
l)ut  they  arc 
rencc,  wliich 
ractcr,  since 
cases.  "In- 
dc fined  as  a 
i  in  iucrrin^ 

a  j)hen()nie- 
all  instances 

resemble  the 
jrial   circum- 

nce  proceeds 

^Ievertheless, 

tlie  nature  of 

ne  insistence 

me  identical 

in  all  the 

rom  one  to 

lat  was  said 

he  possihle 

hat  is  false 

I's  doctrine, 

cular  fact  to 

ruths. 

lars.  — "Not 
iculars,  with- 


t 


out  passing  throui^h  <:jencrals,  l)ut  we  perpetually  tlo  so 
reason.  All  our  earliest  inferences  arc  of  this  nature. 
From  the  first  dawn  of  intelligence  we  draw  inferences, 
hut  years  elapse  hefore  we  learn  the  use  of  jiijencal 
laUj^uaf^c.  The  child,  who,  having  hurned  his  fingers, 
avoids  to  thrust  thr  -i  again  into  the  fire,  has  reasoned 
or  inferred,  thouL;h  he  never  thought  of  the  general 
ma.xim,  Fire  burns.  He  knows  from  memory  that  he 
lias  been  burned,  and  on  this  evidence  believes,  when 
he  sees  a  candle,  that  if  he  puts  his  finger  into  the  flame 
of  it,  he  will  be  burned  again.  He  believ(;s  this  in  any 
case  which  happens  to  arise,  but  witho*'  looking  in 
each  instance  beyond  the  present  case.  \\q.  not  gen- 
eralizing; he  is  inferring  a  j^articular  f  \-i  j.  irticulars. 
...  It  is  not  only  the  village  matron,  .wv  when  called 
to  a  consultation  on  the  case  of  a  neighbour's  child,  pro- 
nounces on  the  evil  and  its  remedy  e  .  he  recollection 
and  authority  of  what  she  accounts  the  similar  ease  of 
her  Lucy.  We  all,  when  we  have  no  definite  maxims 
to  steer  by,  guide  ourselves  in  the  same  way."  * 

The  doctrine  as  thus  stated  by  Mill  is  the  extreme 
opposite  of  Rationalism.  Not  only  are  all  general 
propositions  derived  from  observation  of  particular  in- 
stances, but  they  play  no  part  in  the  process  of  infer- 
ence proper.  All  reasoning,  according  to  this  account, 
is  based  on  the  perception  of  resemblance  between 
individual  cases.  No  common  nature  or  general  prin- 
ciple seems  necessary  to  unite  the  latter  into  a  .system. 

Nevertheless,  it  must  be  confessed  that  Mill's  statc- 


»Mill,  lo>^ic,  15k.  II.  a..  III.  §  v 


I 


I 

'  A 

■i 


342 


RATIONAI.   AND    KMl'IRICAL  TIIKORIKS 


ment  affords  an  excellent  account  of  many  of  our 
ordinary  inferences.  We  may  accept  it,  however,  as  a 
description  of  fact  without  committinj:;;  ourselves  to  the 
theory  which  it  contains.  That  is,  it  will  still  be  neces- 
sary to  ask  if  inference  is  not,  after  all,  based  on  the 
jierception  of  some  [;eneral  law  or  principle,  although 
it  is  not  always  possible  to  formulate  the  nature  of 
the  latter.  It  does  not  seem  to  me  that  the  nature  of 
the  inference  in  the  cases  cited  is  completely  described 
when  it  is  said  to  be  a  passage  from  one  particular 
case  to  another  which  resembles  it.  For  it  is  necessary 
to  look  further,  and  to  see  what  is  iuip/icii  in  the  fact 
that  one  case  is  perceived  to  resemble  another.  When 
the  child  [)erceives  that  the  bright  object  before  him 
resembles  something  which  previously  gave  him  pain, 
he  has  gt)t  beyond  the  merely  indivitlual  aspect  of 
things,  and  is  beginning  to  regard  them  as  types  or 
instances  of  a  general  law.  Of  course,  the  child  is 
not  fully  conscious  of  any  general  principle.  He  does 
not  separate  the  latter  from  its  embodiment  in  the  par- 
ticular case,  or  put  it  into  language  even  to  himself. 
Ikit,  in  order  to  infer,  one  must  take  the  individual 
case  as  something  more  than  a  mere  particular,  as  this 
which  is  oidy  here  and  now.  In  the  child's  perception 
of  resemblance  between  the  present  object  and  the  one 
previously  experienced,  there  is  an  implicit  reference  to 
a  permanent  type,  or  identity  which  persists  through 
the  two  cases.  In  other  words,  when  one  asks  what  a 
perception  of  resemblance  means,  one  sees  that  it  im- 
plies an  apprehension  on  the  part  of  intelligence  of 
something    which    is    more    than    merely    momentary. 


§91.     IKOM    rARTlLULARS  TO    PARI  KULAKS         343 


•m        ^ 


The  same  quality  or  other  clement  which  is  found  in 
that  object  is  also  found  in  this.  And  the  inference 
proceeds,  that  object  was  hot,  therefore  this  object 
(having  the  same  general  nature,  or  being  of  the  same 
type)  is  also  hot.  It  is,  of  course,  frequently  impossible 
to  formulate  clearly  the  nature  of  the  principle  upon 
which  we  proceed,  antl,  in  cases  like  those  cited,  one  may 
not  be  aware  that  it  is  present.  Hut,  I  hojie,  it  will  now 
be  clear  that  even  in  such  instances  the  inference  is 
based  upon  a  permanent  nature  present  in  the  two  cases. 
We  have  already  seen  that  where  such  an  identical  link 
is  not  present,  it  is  impossible  to  pass,  by  means  of  in- 
ference, from  a  knowledge  of  one  thing  to  another.  As 
mere  particulars,  two  phenomena  occurring  at  different 
times  are  entirely  isolated,  and  have  nothing  to  do 
with  each  other.  I^ut  as  pieces  of  knowledge,  facts 
which  have  been  constituted  by  the  interpreting  func- 
tion of  Judgment,  they  arc  bound  together  by  a  com- 
mon principle,  the  nature  of  a  whole  or  system.  This 
principle  is,  indeed,  not  anything  (r/^ar/  from  the  facts 
connected,  or  in  any  way  prior  to  them  ;  but  neverthe- 
less something  without  which  it  would  be  impossible  to 
understand  their  connection. 

The  conclusion  of  the  matter,  then,  is  that  we  never 
reason  from  one  bare  particular  to  another  particular. 
More  than  that,  we  may  say  a  fact  which  is  merely 
particular  —  something  which  is  only  here  and  now  — 
has  no  existence  in  knowledge.  For  knowledge  lays 
hold  of  the  universal  aspect  of  things,  their  permanent 
significance.  Intelligence  sees  the  universal  or  typical 
nature  in  what  is  for  sense  a  fleeting  phenomenon.     It 


M 


.^mwm^. 


344 


RATIONAL   AND    KMIMKICAI,    llli:<  )UIi:s 


is  only  when  the  facts  of  sense  arc  intcr[)rete(l  in  this 
way,  wlien  their  real  nature  is  apprehended  by  thought, 
that  they  can  bo  said  to  be  known  at  all.  Knowled};e 
sees  the  universal  in  the  particular,  or  reads  the  i)artic- 
ular  as  a  case  of  the  universal.  And  when  thus  inter- 
preted, the  j)articular  ceases  to  be  a  bare  particular,  and 
becomes  an  individual  with  a  permanent  nature  of  its 
own.  WMien  one  reasons  from  an  individual  case,  then, 
it  is  the  universal  or  typical  nature,  not  the  particular 
or  momentary  existence,  upon  which  the  inference  pro- 
ceeds. If  there  were  any  merely  particular  facts  in 
knowledge,  we  could  never  reason  from  them.  But,  as 
has  been  shown,  the  so-called  particular  facts,  as  ele- 
ments of  knowledge,  possess  a  universal  or  typical  as- 
pect in  virtue  of  which  alone  inference  is  possible. 


» 


ll 

1 

\k 

t '   \ 

i 

■  "•  si 

wf 

§  92.  Reasoning  from  Individual  Cases  to  a  Universal. 
— There  remains  another  question  which  is  very  closely 
related  to  the  points  already  discussed  in  this  chapter. 
We  must  admit  that  in  inductive  inference  at  least  the 
starting-point  is  individual  instances,  though,  as  the  last 
section  showed,  the  latter,  as  used  in  reasoning,  are 
something  more  than  mere  particulars.  The  problem 
which  meets  us,  however,  is  this :  How  is  it  ever  pos- 
sible to  get  a  universal  conclusion  from  individual 
instances  ?  It,  of  course,  frequently  happens  that  we 
cannot  examine  all  the  cases.  What  right  then  have 
we  in  these  circumstances  to  state  our  conclusion 
generally  —  to  assert,  for  example,  that  */?//  men  are 
mortal,'   or   '  all  mosses   cryptogams  '  .-* 

It  is  often  said  that  in  such  cases  the  general  con- 


lies 

ctcd  in  this 
by  thou^lit, 

Kno\vlc(l<;c 
i  the  partic- 

thus  intcr- 
rticuhir,  and 
laturc  of  its 
I  case,  then, 
le  particular 
fcrcnce  pro- 
lar  facts  in 
im.  But,  as 
acts,  as  elc- 
ir  typical  as- 
)ossiblc. 

a  Universal. 

very  closely 
his  chapter, 
at  least  the 

as  the  last 
soiling,  are 
he  problem 
t  ever  pos- 

individual 
ins  that  we 

then  have 

conclusion 
ill  men  are 

eneral  con- 


§92.     FROM    PAUrU  UI.AKS    D )   A   UMVKUSAL         345 

elusion  is  never  more  than  probable,  and  that  its  proba- 
bility increases  directly  in  proportion  to  the  number  of 
instances  examined.  Thus  if  A  and  H  are  conjoined  only 
once  in  my  experience,  it  is  very  improbabh^  that  the 
connection  is  a  universal  and  essential  one.  Hut  if  they 
are  found  together  ten  times,  the  proposition,  '  A  is  \\ ' 
begins  to  have  probability,  which  is,  of  course,  greatly 
increased  (without  ever  becoming  more  than  probable 
however),  if  the  conjunction  is  observed  a  hundred,  or  a 
thousand  times.  Now,  there  can  be  no  doubt  that  the 
frequency  of  conjunction  is,  to  a  certain  extent,  a  prnc- 
tical  test  of  real  or  universal  connection.  Helief,  as  a 
psyclioloi^ical  fact,  is  engendered  by  frecpiency  of  repeti- 
tion. But  the  causes  of  our  belief  are  here,  as  in  many 
cases,  quite  different  from  the  real  or  logical  grounds. 
Tiie  fact  that  two  jihenomena  have  occurred  together  a 
hundred  times,  /;/  itself  affords  no  loi^iail  ij^round  for 
affirming  a  universal  connection  between  them,  or  that 
they  will  be  connected  the  hundred  and  first  time.  Of 
course,  as  we  have  said,  psycJioloij^ical  belief  or  expecta- 
tion would  be  engendered  by  the  freciuent  conjunction  ; 
but  the  latter  would  supply  no  real  or  logical  grounds. 
Practically,  we  are  more  certain  to  be  right,  if  we  gen- 
eralize on  the  basis  of  a  large  number  of  observation.s, 
than  if  we  proceed  on  the  authority  of  a  smaller  num- 
ber. 15ut,  as  affording  loij^ica/  justification  for  our  pro- 
cedure, a  hundred  instances  (if  they  are  merely  counted) 
are  n    better  than  one. 

The  truth  is  that  a  general  conclusion  does  not  de- 
pend for  its  logical  justification  upon  the  number  of 
instances  observed.     Inference  is  not  a  matter  of  count- 


•t* 


^1 


I 


U 


k    h 


► 

1 

t  ! 


346 


RATIONAL   AM)    KN"MRICAL    TIIIIORIKS 


iiifj^  instnnccs  at  all,  but  is  an  intellectual  insight  into 
the  nature  of  a  general  law  or  principle  of  connection. 
The  problem  of  inductive  inference  is  to  discover  this 
principle  in  the  individual  case,  to  penetrate  beneath 
the  surface,  and  read  out  of  the  individual  phenome- 
non its  real  meaning  or  significance.  To  accomplish 
this  usually  requires  an  examination  of  many  particu- 
lar cases.  We  have  more  chances  of  learning  the 
secret  fully  if  we  take  as  wide  a  survey  as  possible 
of  the  facts.  A  generalization  based  upon  a  small 
number  of  observations  is  pretty  sure  to  be  incorrect 
or  inaccurate.  I^ut  though  of  such  great  practical  im- 
portance, the  number  of  instances  is  logically  indiffer- 
!  ent.  The  essential  point  is  to  detect  the  general  law  or 
,princii;)le,  and  for  this  purpose  one  case  may  conceiva- 
bly be  as  good  as  a  hundred.  Inductive  iriference, 
then,  is  not  a  j^rocess  of  passing  from  a  certain  number 
of  cases  to  a  general  conclusion  which  always  remains 
probable  because  it  has  no  proper  justification.  But  its 
real  nature  consists  in  the  vdiscovery,  through  the  aid  of 
examples,  of  a  universal  law  of  connection.  We  have 
already  shown  the  part  which  the  constructive  imagina- 
tion, guided  by  Analogy,  i)lays  in  reaching  this  result 
(cf.  §§60,63). 

It  r.iiist  1)C  admitted  that  there  are  many  cases  where  it  is  Impossi- 
ble to  j^it  beyond  the  fact  that  two  phenomena  arc  constantly  con- 
joined in  our  experience.  Tiie  ".^rounds  wliich  should  make  this  f  ict 
intelligible  lie  Ijeyond  our  ken.  L'nder  circinnstances  of  this  kind, 
we  are,  of  course,  com[)elle(l  to  act  on  the  presumption  that  tiie  same 
order  of  events  will  continue  to  obtain.  We  may  lind  that  a  certain 
medicine  is  followed  l)y  certain  physii)lo^ical  conseciuences,  without 


) 


\ 


f 


[ES 


§92.     IROM    PARTICULARS  TO   A    UNIVERSAL        347 


insight  into 
connection, 
iscovcr  this 
ate  beneath 
il    piienomc- 

acconiphsh 

my  particu- 

carning  the 

as  possible 

on    a    small 

be  incorrect 

^rdc/icdl  im- 

tl/y  iudiffer- 

neral  law  or 

ay  conceiva- 

^    inference, 

ain  number 

ays  remains 

Dn.     But  its 

h  the  aid  of 

We  have 

ve  imagina- 

this  result 


i>  it  is  inipossi- 

DiisUiutly  Qow- 

iiKiUe  this  fict 

of  this  kind, 

that  the  same 

that  a  ct'itain 

■nccs,  vvilhout 


beiiif;  able  to  discover  anythiiij;  rejj;ardin<;  the  \v.i\  in  whicli  the  lat- 
ter have  been  produced.  .\iul  we  may  contidently  predict  that  the 
same  results  will  lullow  in  a  uew  case  where  the  same  meiiicine  has 
been  }fiven.  Hut  it  must  be  noticed  that  this  is  not  the  iileal  of  rea- 
soning. Knowledge  of  the  kind  we  have  described  is  merely  em- 
pirical, follows  a  rule  of  thumb  without  being  able  to  give  any  account 
of  itself.  Moreover,  even  in  such  cases,  it  is  always  a.ssumed  that 
there  is  some  general  principle  or  law  which  may  yet  be  iliscovered, 
and  which  is  capable  of  explaining  the  facts  known  empirically. 

References 

J.  S.  Mill,  Loi^it,  Bk.  II. 

H.  Spencer,  rriiiciph's  of  J\yi^ioI(\i^}\  §  208. 

VV.  James,  IVie  Prim i pics  of  Psyiholoi^y,  \'ol.  11.  Ch.  .XXVIII. 

B.  IJcsanquet,  / oi;h,  Vol.  II.,  pp.  176  179. 


'i« 


l(^ 


QUESTIONS   AND   EXERCISES 


INTRODUCTION 


Chaptkr  I.  —  The  Staiuipoint  and  Problem  of  Logic 


% 


% 


J 


V 


*.|    I; 


H 


1.  What  arc  some  of  the  main  characteristics  of  thought  or 
thinking? 

2.  l'Ai)lain  the  use  of  the  xerb  to  think  in  each  of  the  fol- 
lowing sentences  :  '  I  do  not  know,  but  I  think  so  ; '  *  If  you 
think  the  matter  over,  you  will  come  to  the  same  conclusion.' 

3.  '  Words  and  phrases  are  often  repeated  without  reflection, 
and  their  very  familiarity  is  likely  to  jirevcntus  from  attempting 
to  understand  exactly  what  ideas  they  represent.'  Give  illus- 
trations of  this  fact. 

4.  What  do  you  mean  by  a  science?  TTow  does  '  scientific  ' 
knowledge  differ  from  the  knowledge  of  ordinary  life? 

5.  What  is  the  meaning  (>f  the  word  'law'  in  the  phrase 
*a  law  of  thought '?  Compare  the  use  of  the  word  in  such  ex- 
pressions as  '  laws  of  nature,'  *  the  laws  of  the  ian('.' 

6.  Is  it  true  that  Logic  and  Psychology  have  the  same 
subject-matter? 

7.  F-xplain  carefully  how  the  problem  of  Logic  differs  from 
that  of  Psychology. 

S,  If  we  i)arallel  Psychology  with  Mori)hology,  and  Logic 
with  Physiology,  what  mental  science  will  correspond  to 
Kmoryology? 

9.  Illustrate  by  means  of  examples  not  used  in  ine  text  the 
relation  m  whi(  h  science  and  art,  or  theory  ;md  i)ra(  tice,  stand 
to  each  other. 

34S 


.'  ^ 


\:,'i 


()Ui:STI{)NS    AND    KXEKCISES 


349 


ISES 


of  Logic 
of  lliouglU  or 

Lch  of  the  fol- 

so  ;'  Mf  you 

conclusion.' 

lout  reflection, 

oni  attempting 

Give  illus- 

)cs  *  scientific ' 
ife? 

n  the  phrase 
(1  in  such  ex- 

ivc   the    same 

c  differs  from 

jy,  and  T.ogic 
:orrespond    to 

in  inc  text  the 
n.u  lice,  stand 


10.  Criticise  the  following  statement:  '  Logic  is  not  only  a 
science  ;  it  is  also  an  art,  for  it  teaches  us  to  reason  correctly.' 

11.  What  part  does  Introspection  play  in  investigating  logi- 
cal questions? 

12.  In  what  sense  may  we  say  that  the  rccoixls  of  everything 
wliich  the  human  race  has  accomplished  form  the  material  of 
Logic? 

CiiAi^rrR  IL — Historical  Sketch 

1.  'The  sciences  have  arisen  in  response  \.()  the  {practical 
needs  of  mankimi.'  Is  this  statement  confirmed  by  the  history 
of  the  origin  ami  development  of  Logic? 

2.  'Since  each  individual  sees  things  from  his  own  point  of 
view,  there  is  therefore  nothing  really  true  in  itself,  or  good  in 
itself.'  Give  some  illustrations  of  the  former  part  of  this  state- 
ment. What  term  would  you  use  to  tlescribe  the  theory  which 
the  sentence  expresses  ? 

3.  ICxplain  what  is  meant  by  tho  statement  that  Socrates 
and  PI  ito  found  a  standard  of  truth  and  of  conduct  in  the 
Concept. 

4.  Why  was  it  not  possible  for  Aristotle  to  Iny  down  a  com- 
plete theory  of  Inductive  Reasoning? 

5.  What  is  Mill';;  theory  regarding  liie  relation  of  Induction 
anil  l)edu(  tion? 

6.  Describe  the  standpoint  of  Modern  Logic. 

PART   L  —  TiiK  Svi.i.ociSMs 
CHArrr.R  III. —  The  SyUogistn  and  it-;  Parts 

1.  Describe  the  general  pur]K)se  and  nature  of  the  syllogism. 

2.  What  is  the  prin<  ij)le  ujton  which  syllogistic  reasoning 
depends?  Why  is  it  impossible  to  reason  if  this  prin(  iple  is 
violated? 


\\i 


V 


fi 


t 


id 

1 

t 

IH 

W^l 

li 


>  r 


I  i 


1 1 


'ii 


I  » 


•! 


.\ 


350 


(,)UKSriO\S   AND    KXEKCISKS 


3.  l^xplain  the  distinction  between  the  formal  and  real  truth 
of  an  argument. 

4.  Arrange  the  following  sentences  as  logical  propositions, 
pointing  out  the  U)gical  Subject  and  the  Predicate  in  each 
case  :  — 

{(i)    Learning  taketh  away  the  wildncss  of  men's  minds. 

(/' )   Dissipation  wastes  health. 

(i- )  The  exposition  of  a  i)rinciple  indirectly  contributes  to 

its  proof. 
{{/)  To  me  the  meanest  flower  that  lives  can  give  thoughts 

that  do  often  lie  too  deej)  for  tears. 
(r)  The  Alps  consist  of  several  parallel  ranges. 
{/)  The  travellers  had  found  the  city  in  ruins. 

5.  Point  out  the  Premises  and  Conclusion  in  the  following 
arguments,  and  supply  Ci.iy  premise  which  may  be  wanting  :  — 

(</)  He  is  not  indifferent  to  money ;  for  he  is  a  sensible 
man,  and  no  sensible  man  despises  money. 

(^)  All  human  productions  are  liable  to  error,  and  there- 
fore all  books,  being  human  productions,  are  liable 
to  error. 

(c)   All  that  glitters  is  not  gold  ;  for  brass  glitters. 

(//)  All  bodies  which  move  round  the  sun  are  planets; 
therefore  the  earth  is  a  jjlanet. 

(^)  Platinum  is  a  metal,  and  therefore  combines  with 
oxygen. 

6.  Mow  does  Jevons  describe  Simple  Apprehension?  Is  it 
possible  to  maintain  that  Apprehension,  Judgment,  and  Rea- 
soning are  three  distinct  operations  of  mind  ? 

Chaitkr  IV.  —  Terms 

I.  Difitinguish  in  the  following  list  the  terms  which  are 
usually  (i)  Singular,  (2)  Oeneral,  and  (3)  Collective.     If  any 


\v^ 


gUESriONS   AND    EXERCISES 


351 


iiicl  real  truth 

propositions, 
icate   in   eacli 

en's  minds, 
contributes  to 
give  thoughts 


;es. 

I)S. 


the  followin" 
I  wanting  :  — • 

!  is  a  sensible 

loney. 

or,  and  there- 

ons,  are  liable 


liters, 
arc  planets ; 

ambincs  with 

•nsion?     Is  it 
nt,  and  Rea- 


ls which    are 
live.     If  any 


term  may  belong  to  more  than  one  class,  explain  and  illustrate 
its  various  uses  :  — 


Niagara  I'alls, 

gold, 

chair, 

a  pack  of  cards, 


an  oak  tree, 
a  (kincing  party, 
the  Unitcil  States, 
city, 


tlie  United  States  Navy, 

Iirooklyn  I'lridgc, 

humanity, 

the  centre  of  the  earth. 


2.  ICxplain  and  illustrate  the  ambiguity  in  the  use  of  the 
word  'all.' 

3.  In  what  two  ways  are  the  words  .Abstract  and  Concrete 
used?  In  what  sense,  if  at  all,  can  we  say  that  Psychology  and 
Logic  are  '  abstract  '  sciences? 

4.  Distinguish  carefully  between  Contradictory  and  Op[)0- 
site  terms. 

5.  What  are  Correlative  terms?  (live  at  least  three  ex- 
amples. 

6.  Mention  the  synonyms  for  Intension  and  I'xtension. 

7.  Explain  the  Mxtensional  and  Intensional  use  of  the  fol- 
lowing terms  :  — 


metal, 
justice, 


chair, 
student. 


rri.m, 
John  Jones, 


Casar, 

islaiitl, 


superstition, 
emperor. 


8.  Criticise  the  statement  that  '  I-'xtension  ai:  I  Intension 
stand  in  inverse  ratio  to  each  other.'  What  truth  does  it  con- 
tain? 

9.  Invent  a  scries  of  at  lenst  six  terms  which  may  be  ar- 
ranged hO  as  gradually  to  increase  in  Extension. 

10.  What   may  be  said  in  reply  to  Mill's  c*       -ntion  that 
%           proper  names  are  non-connotative  ? 


Chai'ITR  V.  —  Difini/ion  and  Di        n 

1.  Why  is  Definition  necessary? 

2.  What  is  the  distinction  between  extensive  .md  intensive 
definition?     What  is  a  verbal  definition? 


■m 


^l 


352 


QI'KSTIONS   ANT)    KXKKriSKS 


;\.    Ill    what   two    ways    may   \vc    ronrcive   the   problem   of 
Dcfiiiilion  ? 

4.  What  do  you  nn(lcrstan('  hy  the  Socratic  Dialeclic?    Kx- 
plairi  its  purpose  and  mode  of  procedure. 

5.  I'Ai)lain  the  terms  :  — 


genus, 
species, 


(liftcrcntia, 
suinmuiu  j^cnus, 


mhma 

sui  j^encrtiw 


6.  Criticise  the  following;  definitions,  pointing  out  whai  riles, 
if  any,  are  violated  by  them  :  — 

( i)  Lof^ic  is  the  science  of  thou!j;ht. 

(2)  A  power  is  a  f(jn  e  which  tends  to  pro<Itirc  motion. 

(3)  'Pin  is  a  metal  hghtor  than  gold. 

(4)  A  gentleman  is  a  man  who  has  no  definite  means  of 

support. 

(5)  The  body  is  the  emblem  or  visible  garment  of  the 

soul., 

(6)  Man  is  a  vertebrate  animal. 

(7)  Thunder- bolts  are    tlie   winged   messengers  of  the 

gods. 

(8)  A  moral  man  is  one  who  does  not  lie  or  steal  or  live 

inteniperately. 
^^^9)   Cheese  is  a  caseous  preparation  of  milk. 

(10)  Evolution  is  to  be  defined  as  a  contimiou'4  rhange 

from  indcfiniLe  incoherent  homogeneity  to  tkfmitc 
coherent  heterogeneity  of  structure  and  fanction, 
through  successive  differentiations  and  migra- 
tions (Spencer). 

(11)  Oats  is  a  grain  which  in  England  is  generally  given 

to  horses,  but  in  Scotland  supjjorts  the  people. 

7.  ('live  examples  of  terms  which  are  indefinable,  ami  ex- 
plain why  this  is  the  case.  What  is  the  distinction  lietwecn 
Description  antl  logical  Definition? 


t 


()Ui>ri().\s  AM)  i;xi;kcises 


6i 


e   problem   of 
•ialcclic?    Kx- 


(S.    I  )t'rmc  the  fulluwiiig  terms  by  giving  the  genus  and  dif- 


la  sprcks, 

out  what  rules, 


M  It  ire  motion. 
Initc  meaas  of 
garment  of  the 

angers  of  tlie 
jr  ^teal  or  live 

ilk. 

tiniious  chanpc 
ity  to  dirfinitc 
and  fanction, 
ami    int^T^- 

t  nerally  given 
the  people. 

ruble,  ami  cx- 
rtion  lietwccn 


ic 


fcrenti.i  :  — 

science, 
triaii]4k-, 


'<H 


rcpulilic, 
munarcliy, 


psych-.lMjjy, 
^ol'l  staiidartl. 


island, 
iinpinl  'Inly. 


().  Mxamine  the  following  Divisions  and  point  out  whic  h  are 
logiial  and  which  are  not  :  — 

(i)  Living  l)eings  into  moral  and  innnoral. 

(2)  Men  into  saints  ami  sinners. 

(3)  Religions  into  true  an«l  false. 

(4)  Man  into  c  ivili/ed  and  black. 

(5)  Cleometrical   figures  into  rectilinear  and   non-recti- 

linear. 

(6)  SubstaiK  es  into  material  ami  s[jiritual. 

(7)  Metals  into  white,  heavy,  and  precious. 

(S)   ICleuKMitary   mental   processes    into  sensations   ami 

affections. 
{())   Sludcnts  into    those  who  arc   idle,   those  who    are 

athletic ,  and  those  who  ar.  il;  (i^ent. 
(10)    i)Ooks  into  scientific  and  non  .  cientific. 

ClIAnKK   VI.         /*J(>/;>il//i>flS 

1.  What  is  a  projMsition?  Iti  what  sense  may  a  proposition 
be  said  to  have  i)arts? 

2.  Distinguish  between  Categorical  and  < 'onditional  i)ropo- 
silions. 

3.  What  is  raeanl  by  (</)  the  Quality,  and  {/')  the  ()iiantity, 
of  propositions? 

4.  ArranL;e  the  following  sentences  in  the  form  of  logical 
propositions,  and  indicate  the  (Jualily  and  (Juantil\  of  cacli 
categorical  proposition  by  the  uac  of  the  letters  .\,  \i,  I, 
and    O:  — 

2A 


354 


(QUESTIONS   AM)    KXr.kCISKS 


1  1 


§        f 


Hi 


ii 


( 1 )  Urcvily    has    to   l)e  sou^Mil   willKnil  sacrifu  ing  pcr- 

spic  uity. 

(2)  I!c-   that  (l(K'th   tliesc  things  is  like  to  a  man  that 

biiildclh  his  house  111)011  a  rock. 

(3)  Socrates  deckired  knowled^'c  to  be  virtue. 

(4)  l*hosphorus  does  not  (hssolve  in  water. 

(5)  Nearly  all  the  troops  have  left  the  town. 

(6)  Only  ignorant  persons  hold  .such  opinions. 

(7)  Kew  persons  are  j)roof  against  temptation. 

(8)  Over  the  mountains  poured  the  barbarian  horde. 

(9)  Ivxcept  ye  repent,  ye  shall  all  likewise  perish. 

(10)    Neither  gold  nor  silver  is  the  pro[)er  standard  of 
value. 

5.  How  does  formal  logic  intcrp'^et  the  relation  between  the 
sM])ject  and  predicate  of  a  categorical  pro|)osition?  Does  this 
view  do  full  justice  to  the  signification  of  propositions? 

6.  How  would  you  represent  by  means  of  circles  the  propo- 
sition, 'gold  is  the  mo.'>l  precious  metal'? 

7.  Wiial  do  you  mean  by  the  distribution  of  terms?  Explain 
why  negative  propositions  distribute  the  i)redicate,  while  affir- 
malivc  jjropositions  do  not. 

<S.  State  j>rerisely  what  is  asserted  by  Proposition  I.  What 
.'.'•ms  may  tin-  diagrams  which  represent  this  proposition 
assume? 

("iiAi'TKK  VH. —  T/w  ////<r/>/r /(I //(>//  of  Propositions 

1.  Why  is  it  better  to  speak  of  the  Interpretation  of  projx)- 
sitions  than  to  use  the  term  '  Mediate  Inference'? 

2.  What  is  meant  by  the  Opposition  of  [)ropositions? 

3.  Ivxplain  the  distinction  between  Contrary  and  Contradic- 
tory propositions. 

4.  If  proposition  O  is  false,  what  is  known  regarding  the 
truth  or  falsity  of  A,  K,  and  1  ? 


gUKSTlUNS   .\S[)    1  XKKCISKS 


355 


regard ini:  llio 


5.  What  is  tlic  simpK'st  propo'.itioii  which  must  be  cstal)- 
li^hcl  in  order  to  (hMprnve  the  lollowinj^  statements:  (</)  All 
men  desire  wealth.  (/')  No  man  is  perfectly  happy,  (r  )  Some 
knowledge  is  .vot  of  any  value.  (//)  Tain  alone  i.s  evil.  (')  .Ml 
is  not  lost. 

6.  (live  the  contrary  (or  sul)-( ontrar)  ),  and  the  (ontradic  torv 
of:  (<0  .Ml  metals  are  elements.  (/')  NO  (oward  need  applv. 
(<•)  Socrates  was  the  wisest  man  in  Athens.  (</)  Not  all  men 
are  hrave.      (f)  No  man  but  .1  traitor  would  have  dom-  this. 

7.  (live  the  ( )b\erse  of  the  followin^  propositicMis  :  — 

(  I  )  All  horses  are  (|uadrupeds. 

( 2  )  ( lood  men  are  chant. d)le. 

(3)  .None  of  the  cajjtives  escaped. 

(4)  Some  of  the  planets  are  not  larger  than  the  earth, 
^■(s)  Some  students  do  not-fail  in  anything. 

(6)  .Ml  laiglish  dukes  are  members  of  the  I  louse  of  Lords. 

(7)  No  illogical  author  is  truly  scientific. 

8.  Convert  in  at  least  one  way  :  — 
^  (i)   .-Ml  men  are  rational. 

(2)  Some  metals  are  readily  fusible. 

(3)  Perfect  happiness  is  imi)ossible. 

(4)  None  of  the  capti\es  cscapeil. 

(5)  Tneasy  lies  the  lu  ad  that  wears  a  crown. 

(6)  Not  every  man  ( ould  stand  such  hardships. 
)^  (7)  None  but  the  brave  deserves  the  fair. 

(8)  Phosphorus  will  not  dissolve  in  alcohol. 

(9)  Hydrogen  is  the  lightest  body  known. 
(10)  'The  world  is  my  idea. 

9.  Convert  by  contraposition  :  — 

( 1 )  .Ml  honest  men  are  of  this  opinion. 

(2)  Oxygen  can  be  prepared  by  heatmg  potassium  chlo- 

rate in  a  thin  glasb  flask. 


•m 


Ui 


356 


()Ui':s'n()Ns  AND  i:xi:utisi:s 


(3)  Some  of  the  enemy  were  not  prepared  to  surrender. 

(4)  Not  all  who  canie  to  scoff  remained  to  pray. 

(5)  A  triangle  is  a  plane  fij;iire  Itounded  by  three  straight 

lines. 

(6)  The   return  of  peace  had  given  fresh  confidence  to 

the  government  party. 

10.  Describe  the  logical  relation  between  each  of  the  four 
following  propositions :  — 

(1 )  All  substances  which  are  material  possess  gravity. 

(2)  No  substances  which  possess  gravity  art'  immaterial, 

(3)  Some  sul)stances  which  are  immaterial  do  not  possess 

gravity. 

(4)  Some   substances  which  tlo  not  possess  gravity  ar*; 

immaterial.      (Jevons.) 

11.  What  is  the  ( )bverse  of  the  Converse  of,  '  None  of  the 
planets  shine  by  their  own  light '? 

12.  C'un  we  logically  conclude  that  because  heat  expands 
bodies,  therefore  cold  contracts  them?     (Jevons.) 

13.  ^Vhat  is  the  logical  relation,  if  any,  between  the  two 
assertions  in  i'roverbs  xi.  i,  *  A  false  balance  is  an  abomination 
to  the  Lord  ;  but  a  just  weight  is  his  delight '?     (Jevons.) 

CiiAiTKK  VIII. —  The  Syllogism  and  its  Rules 

1.  What  is  the  relation  of  the  Proposition  and  the  Syllo- 
gism ? 

2.  What  is  the  function  of  the  Middle  Term  in  a  Syllogism? 

3.  I  low  are  the  major  and  minor  terms,  and  the  major  an^^ 
minor  i)remises  of  a  Syllogism  distinguished? 

4.  Prove  the  seventh  and  eighth  canon  of  the  Syllogism, 
(<0  by  means  of  the  previous  rules,  and  {l>)  by  the  use  of 
circles. 


gUKSriONS   AM)    KXKKvlSliS 


35: 


.o  surrender. 


5.  (!()nstruct  an  ar^'umciU  to  illustrate  '.\c  fallacy  of  iunbigu- 
ous  middle  term. 

6.  Arrange  the  followiiiLC  ar},'unu'nts  in  tlu  regular  logical 
order  of  major  premise,  mitior  premise,  and  conclusion,  and 
examine  them  to  sec  whether  they  conform  to  the  canons  of 
the  Syllogism  :  — 

( 1 )  (lold  is  not  a  compound  substance  ;  for  it  is  a  metal, 

and  none  of  the  metals  are  compounds. 

(2)  All  national  holidays  are  hank  holidays,  the  bank  will 

therefore  be  closed  on  the  fourth  of  July. 

(3)  .All    cruel    men    are   cowards,    no    college    men   are 

cruel,  therefore  no  college  men  are  cowards. 

(4)  Some  useful  metals  are  becoming  rarer.     Iron  is  a 

useful  metal,  and  is  therefore  becoming  rarer. 

(5)  This  man  shares  his  money  with  the  poor,  but  no 

thief  ever  does  thi.s,  therefore  this  man   is  not  a 
thief. 

(6)  He  who   is  content   with  what  he  has  is  truly  richr 

An  envious  man  is  not  content  with  what  he  has;V 
no  envious  man  therefore  is  truly  rich.\. 

7.  What  does  the  Figure  of  an  Argument  depend  upon? 
How  do  you  distinguish  the  four  figures? 


••< 


Cn.xn'F.R  IX.  —  T/if  Va/ii/  Moods  and  the  Reduction  0/  Figures 

I.    Arrange  the  followuig  arguments   in   logical  order,  and 
give  the  mood  and  figure  in  each  case :  — 


(I)  X.)  Pis  M, 
Sonic  S  is  M, 
Therefore  some  S  is  not  \\ 


(2)  All  M  is  S, 
Some  M  is  P, 
Therefore  some  S  is  I'. 


2.    Name  the  premises  from  whicli   valid  conclusions  may 
be  drawn,  no  account  being  taken  of  figures  :  — 


v>< 


i^r 


e>    "    "'^^ 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0    !fi 


I.I 


M    12.5 


1.8 


1.25      1.4      1 6 

4 6"     

► 

V] 


<? 


/}. 


% 


/a 


^y..  o>.     ^^' 


/A 


W^'W 


'/ 


Photogi^phic 

Sciences 
Corporation 


33  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  873-4503 


i. 


i/x 


Ws 


IP 


^^^1'  i  3' 


■fl 


m 


m 


3.  Prove  the  special  canons  of  the  fourth  figure. 

4.  'The  middle  term  must  be  distributed  once  at  least.' 
In  what  figures  may  it  be  distributed  twice?  What  is  the 
character  of  the  conclusion  when  this  occurs? 

5.  Prove  generally  that  when  the  major  term  is  predicate  in 
its  premise,  the  minor  premise  must  be  affirmative.^ 

6.  If  the  major  term  be  distributed  in  its  premise,  but  used 
undistributively  in  the  conclusion,  detern^ne  the  mood  and 
figurci 

7.  Explain  why  we  can  obtain  only  negative  conclusions  by 
means  of  the  second  figure  and  particular  conclusions  by  means 
of  the  third  figure. 

8.  What  conclusions  do  AA,  AE,  and  EA  yield  in  the  fourth 
figure  ?     Explain. 

9.  Is  it  possible  for  both  major  and  minor  terms  to  be  par- 
ticular at  the  same  time  in  the  premises?  If  so,  construct  an 
argument  where  this  is  the  case. 

10.  What  do  you  understand  by  Reduction?  Reduce  the 
following  argument  to  the  first  figure  :  — 

No  fixed  stars  are  planets, 

All  planets  are  bri.^ht  and  shining, 

Therefore  some  bright  and  shining  bodies  are  not  fixed  stars. 

Chapter  X.  —  Abbreviated  and  Irregular  Arguments 

I.  Cc.nplete  the  following  arguments,  determine  their  mood 
and  figure,  and  examine  them  to  see  if  they  violate  any  of  the 
rules  of  the  syllogism  :  — 

(i)    Blessed   are   the   meek,   for  they  shall   inherit   the 

earth. 
(2)    He  must  be  a  strong  man,  for  he  was  on  the  crew. 


A^i^y 


QUESTIONS   AND    EXERCISES 


359 


,,     EA,     00. 

re. 

once  at  least.' 
What   is  the 

is  predicate  in 
ive. 
emise,  but  used 

the  mood  and 

conclusions  by 
usions  by  means 

2ld  in  the  fourth 

terms  to  be  par- 
so,  construct  an 

n?    Reduce  the 


(3)  Zoophytes  have  no  flowers  ;   therefore  they  are  not 

plants. 

(4)  None  but  material  bodies  gravitate,  therefore  air  is 

a  material  body. 

(5)  He  has  been  a  politician  for  years,  and  is  therefore 

not  to  be  trusted. 

2.  Illustrate  the  difference  between  the  Progressive  or 
Synthetic,  a  id  the  Regressive  or  Analytic  methods  as  em- 
ployed in  Mathematics  and  Psychology  May  a  science 
employ  both  methods  at  the  same  time 

3.  Break  up  the  concrete  examples  of  Sorites  given  on 
pages  130,   131,  into  syllogisms. 

4.  Show  generally  why  all  the  premises  except  the  first  in 
the  AristoteHan  Sorites  must  be  universal. 

5.  Prove  that  in  the  Goclenian  Sorites  the  first  premise 
alone  can  be  negative,  and  the  last  alone  particular. 

6.  In  the  examples  of  arguments  given  on  page  133,  is  there 
any  middle  term?  If  not,  what  serves  as  the  standard  of 
comparison  ? 


"i: 


Dt  fixed  stars. 

Argnmejiis 

nine  their  mood 
iolate  any  of  the 

hall   inherit   the 
on  the  crew. 


Chapter  XL  —  Hypothetical  and  Disjunctive  Arguments 

I.  What  reasons  are  there  for  classifying  the  disjunctive 
proposition  as  conditional  ? 

1.   What  are  the  rules  of  the  hypothetical  syllogism  ? 

3.  Is  it  ever  possible  to  obtain  a  valid  conclusion  by  deny- 
ing the  antecedent  or  affirming  the  consequent  ? 

4.  Determine  which  of  the  following  hypothetical  arguments 
are  valid  and  which  invaUd ;  then  express  the  latter  in  the 
categorical  form,  pointing  out  what  are  the  categorical  fallacies 
which  result :  — 


'^ 


(i)    If  a  man  is  avaricious,  he  will  be  unhai)py  ;  but  A  is 


w,L,jm. 


360 


QUESTIONS   AND    EXERCISES 


i  , 


m 


unhappy,  and  we  may  therefore  conclude  that  he  is 
avaricious. 

(2)  If  A   is  B,  C  is  I),  l)ut  A  is  B,  therefore  we  may 

conchule  that  C  is  I). 

(3)  If  the  door  were  locked,   the   horse  would  not  he 

stolen  ;  but  the  horse  is  not  stolen,  therefore  the 
door  must  have  been  locked. 

(4)  If  man  were  not  capable  of  progress,  he  would  not 

differ  from  the  brutes  ;  but  man  does  differ  from 
the  brutes,  therefore  he  is  capable  of  progress. 

(5)  If  he  had  studied  his  lesson,  he  would  have  been 

able  to  recite  ;  but  he  was  able  to  recite,  and  there- 
fore must  have  studied  his  lesson. 

(6)  If  it  becomes  colder  to-night,  the  pond  will  be  frozen 

over ;    but    it   will    not    become    colder    to-night, 
therefore  the  pond  will  not  be  frozen  over. 

5.  What  aspects  of  thinking  are  emphasized  by  the  cate- 
gorical and  hypothetical  forms  of  reasoning  respectively? 

6.  How  for  may  the  disjunctive  proposition  be  regarded  as 
an  expression  of  ignorance,  and  what  is  the  justification  for 
the  statement  that  it  involves  systematic  knowledge  ? 

7.  To  what  fallacy  is  the  disjunctive  argument  specially 
liable  ? 

8.  How  would  you  criticise  the  dilemmatic  arguments  given 
on  page  150? 

Chapter  XII.  —  Fallacies  of  Deductive  Reasoning 

1.  What  is  the  distinction  between  errors  of  interpretation 
and  follacies  in  reasoning? 

2.  Why  is  the  detection  of  material  follacies  a  proper  subject 
of  logic? 

3.  If  it  is  true  that  all  the  righteous  people  are  happy,  can 


:lude  that  he  is 


re  fore  we  may 


QUESTIONS   AND    EXKRCISKS 


361 


we  condudc  that  nil  unhappy  iicople  arc  unriL^Mi toons?      Tf  so, 
how  do  we  pass  from  the  first  statement  to  the  second? 

4.  Can  we  proceed  logically  from  the  proposition,  '  all  good 
citizens  vote  at  elections,'  to  '  all  who  vote  in  elections  are 
good  citizens  '? 

5.  Does  the  statement  that  '  some  sciences  are  useful'  justify 
the  proposition  that  'some  useful  things  are  not  sciences'? 

6.  Mention  the  fallacies  of  Equivocation,  and  explain  what  is 
common  to  them  all. 

7.  Explain  the  terms  :  Pcfifio  Principii,  Circuliis  in  prohaiuh^ 
Ar^itmentiiin  ad  lioniincm,  y1rs;inncnfinn  ad popitlum. 

8.  Examine  the  following  reasoning:  * 'The  argument  from 
design  must  be  regarded  as  without  value  ;  for  it  has  been  re- 
jected by  Spinoza,  Kant,  SjKMicer,  and  Darwin.' 


s 


1.4 


ument   specially 


irguments  given 


l\TlSCF,LT.ANEOUS    EXAMPLES 

Arrange  the  following  arguments  whenever  possible  in  regular 
logical  order ;  determine  whether  or  not  they  are  valid  ;  give 
the  mood  and  figure  of  the  valid  categorical  arguments  ;  if  any 
argument  is  invalid,  point  out  and  name  the  fallacy  involved  :  — 

1.  All  virtue  is  praiseworthy,  and  charity  is  a  virtue,  there- 
fore charity  is  praiseworthy. 

2.  All  colours  are  physical  phenomena ;  but  no  sound  is  a 
a  colour,  therefore  no  soimd  is  a  physical  phenomenon. 

3.  Some  minerals  are  precious  stones,  all  topazes  are  pre- 
cious stones,  therefore  some  minerals  are  topazes. 

4.  Some  acts  of  homicide  are  laudable,  therefore  some 
cruel  things  are  laudable. 

5.  If  he  has  found  the  treasure,  he  is  rich;  but  he  has  not 
found  it,  therefore  he  is  not  rich. 

6.  He  must  be  a  Democrat ;  for  all  the  Democrats  believe 
in  Free  Trade. 


362 


QUESTIONS   AND    EXERCISES 


'.  ','! 


'i  i 


7.  If  only  the  ignorant  desjMse  knowledge,  this  man  cannot 
be  ignorant,  for  he  praises  it.     (ICdinburgh,  1892.) 

<S.  Whatever  is  given  on  the  evidence  of  sense  may  be  taken 
as  a  flict ;  the  existence  of  God,  therefore,  is  not  a  fact,  for  it  is 
not  evident  to  sense.     (St.  Andrews,  i8g6.) 

9.  This  explosion  must  have  been  occasioned  by  gunpowder  ; 
for  nothing  else  would  have  possessed  sufficient  force. 

TO.  This  burglary  is  the  work  of  a  professional;  for  an 
amateur  would  not  have  been  half  so  clever. 

11.  No  stupid  person  can  become  President  of  the  United 
States ;  therefore  Mr.  Cleveland  and  Mr.  McKinley  must  both 
be  men  of  ability. 

12.  Since  almost  all  the  organs  of  the  body  have  some  use, 
the  vermiform  appendix  must  be  useful. 

13.  Every  candid  man  acknowledges  merit  in  a  rival,  every 
learned  man  does  not  do  so ;  therefore  learned  men  are  not 
candid. 

14.  Every  book  is  liable  to  error,  every  book  is  a  human 
production,  therefore  all  human  productions  are  liable  to  error. 

15.  Learned  men  sometimes  become  mad;  but  as  he  is  not 
learned,  there  is  no  danger  of  his  sanity. 

16.  If  this  candidate  used  money  to  secure  his  election,  he 
deserved  defeat ;  but  he  did  not  use  money  in  this  way,  and 
therefore  did  not  deserve  defeat. 

1 7.  All  valid  syllogisms  have  three  terms ;  this  syllogism  is 
therefore  valid,  for  it  has  three  terms. 

18.  No  persons  destitute  of  imagination  are  true  poets; 
some  persons  destitute  of  imagination  are  good  reasoners ; 
therefore  some  good  reasoners  are  not  true  poets. 

19.  Only  material  bodies  gravitate  ;  ether  does  not  gravitate. 

20.  In  reply  to  the  gentleman's  arguments,  I  need  onJy  say 
that  two  years  ago  he  advocated  the  very  measure  which  he 
now  opposes. 


T'i 


■wv 


()UESri()XS    AND    I-A'KRCISKS 


is  man  cannot 

2.) 

2  may  be  taken 

:  a  fcict,  for  it  is 

by  gunpowder  ; 

force. 

isional ;    for  an 

t  of  the  United 
inley  must  both 

have  some  use, 

n  a  rival,  every 
d  men  are  not 

ok  is  a  human 
I  Hable  to  error, 
jut  as  he  is  not 

his  election,  he 
1  this  way,  and 

his  syllogism  is 

re  true  poets ; 
3od   reasoners ; 

s. 

s  not  gravitate. 
I  need  only  say 
isure  which  he 


21.  If  he  claims  that  he  did  not  steal  the  goods,  wliy,  T  ask, 
did  he  hide  them  as  no  thief  ever  fails  to  do? 

22.  If  this  therefore  be  absurd  in  fact  and  theory,  it  must 
also  be  absurd  in  idea,  since  nothing  of  which  we  can  form  a 
clear  and  distinct  idea  is  impossible.  (Hume,  Treatise  of 
Human  Nature,^ 

23.  Whatever  is  produced  without  a  cause  is  ])roduced  by 
nothing,  or  in  other  words  has  nothing  for  its  cause.  But 
nothing  can  never  be  a  cause.  Hence  every  object  has  a  real 
cause  of  its  existence.     (Hume,  Treafise.) 

24.  ICverything  must  have  a  cause  ;  for  if  anything  wanted 
a  cause  it  would  produce  itself,  that  is,  exist  before  it  existed, 
which  is  impossible.     (Hume,  Treatise.) 

25.  If  it  be  true,  as  Mr.  Spencer  thinks,  that  the  past 
experience  of  the  race  has  produced  innate  ideas  and  feel- 
ings, Weismann's  denial  of  Use-inheritance  would  be  refuted. 
Certainly,  but  it  is  just  possible  that  Mr.  Spencer's  theory  is 
not  true. 

26.  Democracy  is  not  a  perfect  form  of  government,  for 
under  it  there  are  able  men  who  do  not  get  power  ;  and  so 
it  allows  men  to  get  power  who  are  not  able. 

27.  Of  university  professors,  some  are  zealous  investigators, 
and  some  good  teachers,  A  is  an  excellent  teacher,  and  we 
may  therefore  conclude  that  he  is  not  a  zealous  investigator. 

28.  Seeing  that  abundance  of  work  is  a  sure  sign  of  indus- 
trial prosperity,  it  follows  that  fire  and  hurricane  benefit  in- 
dustry, because  they  undoubtedly  create  work.     (St.  Andrews, 

1895-) 

29.  I  will  have  no  more  doctors  ;  I  see  that  all  of  those  who 

have  died  this  winter  have  had  doctors.     (St.  Andrews,  1896.) 

30.  If  a  man  is  educated,  he  does  not  want  to  work  with  his 
hands  ;  consequently,  if  education  is  universal,  industry  will 
cease.     (London,  1897.) 


^'1 


i^^ 


H' 


3^4 


(,)Ui:srio\s  and  i:xi:rcisi:s 


i'H 


I  h 


m' 


31.  None  l)nt  tlic  wise  arc  good,  and  none  but  the  good  are 
hap]iy,  therefore  none  but  tlie  wise  are  happy.  (ICdinburgh, 
1897.) 

32.  (living  advice  is  useless.  For  either  you  advise  a  man 
what  he  means  to  do,  in  which  case  the  advice  is  superfluous  ; 
or  you  advise  him  what  he  does  not  mean  to  do,  and  the  advice 
is  ineffectual.      (London,  1S97.) 

;^;^.  No  pauper  has  a  vote,  A  B  is  not  a  pauper,  therefore 
he  has  a  vote.     (St.  Andrews,  1897.) 

34.  The  love  of  nature  is  never  found  either  in  the  stupid 
or  the  moral  man,  therefore  stupidity  and  virtue  are  incompati- 
ble.    (Kdinburgh,  1897.) 

35.  Not  all  educated  persons  spell  correctly  ;  for  one  often 
finds  mistakes  in  the  pajiers  of  University  students. 

36.  Free  Trade  is  a  great  boon  to  the  workingman  ;  for  it 
increases  trade,  and  this  cheapens  articles  of  ordinary  con- 
sumption ;  this  gives  a  greater  purchasing  power  to  money, 
which  is  ecpiivalent  to  a  rise  in  real  wages,  and  any  rise  in 
real  wages  is  a  boon  to  the  workingman. 

37.  If  the  train  is  late,  I  shall  miss  my  appointment ;  if  it  is 
not  late,  I  shall  not  reach  the  depot  in  time  to  go  by  it,  there- 
fore, in  any  case,  I  shall  miss  my  appointment. 

38.  He  who  spareth  the  rod  hateth  his  child ;  the  parent 
who  loves  his  child  therefore  spareth  not  the  rod. 

39.  Whatever  tends  to  withdraw  the  mind  from  pursuits  of 
a  low  nature  deserves  to  be  promoted  ;  classical  learning  does 
this,  since  it  gives  us  a  taste  for  intellectual  enjoyments ;  there- 
fore it  deserves  to  be  promoted. 

40.  As  against  the  proposition  that  the  formation  of  public 
libraries  prevents  private  individuals  from  purchasing,  and  so 
decreases  the  sale  of  books,  a  writer  urges  that  whatever 
encourages  the  reading  of  books  encourages  the  buying  of 
books.     It  is  a  library's  purpose  to  encourage  reading,  and 


1*.. 


QUl'SriONS   AND    KXEKCISES 


3OS 


f 


auper,  therefore 


hence  the  net  result  is  rather  to  increase  tlian  to  lessen  pur- 
chases. 

41.  No  reason  however  can  he  !j;iven  why  the  general  haj)- 
])iness  is  desirable,  except  that  each  person,  so  far  as  he 
believes  it  to  be  attainable,  desires  his  own  happiness.  This, 
however,  beinu;  a  fact,  we  have  not  only  all  the  proof  which 
the  case  admits  of,  but  all  which  it  is  possible  to  recpiire,  that 
hapi)iness  is  a  good,  that  each  person's  happiness  is  a  good  to 
that  person,  and  the  general  hapi)iness,  therefore,  a  good  to 
the  aggregate  of  all  persons.     ( Mill's  Utilitarianism.) 

42.  This  man  is  a  Protestant;  for  he  exercises  the  right  of 
private  judgment. 

43.  If  the  orbit  of  a  comet  is  diminished,  either  the  comet 
passes  through  a  resisting  medium,  or  the  law  of  gravitation  is 
partially  suspended.  lUit  the  second  alternative  is  inailmis- 
sible.  Hence  if  the  orbit  of  a  comet  is  diminished,  there  is 
present  a  resisting  medium. 

44.  How  do  we  know  that  our  intuitive  beliefs  concerning 
the  world  are  invariably  true?  Either  it  must  be  from  experi- 
ence establishing  the  harmony,  or  an  intuitive  belief  must  certify 
the  correctness.  Now  experience  cannot  warrant  such  har- 
mony except  in  so  far  as  it  has  been  perceived.  Still  more 
futile  is  it  to  make  one  instinctive  belief  the  cause  of  another. 
Thus  we  cannot  know  that  any  intuitive  belief  is  universally 
valid.     (Bain.) 

45.  Which  of  the  following  are  real  inferences  :  (i)  'This 
weighs  that  down,  therefore  it  is  heavier' ;  (2)  'This  piece  of 
marble  is  larger  than  that,  anil  therefore  is  heavier.' 

46.  The  parts  of  pure  space  are  immovable,  which  follows 
from  their  inseparability,  motion  being  nothing  but  change  of 
distance  between  any  two  things  ;  but  this  cannot  be  between 
parts  that  are  inseparable,  which  therefore  must  be  at  per- 
petual rest  one  amongst  another. 


1,^ 


366 


<)UKSTI()NS   AND   EXKKCISES 


I    i     i 


P- 


'    Jl 


M 


:  i    !  .    ' 

■ 

1 

:.'.        i 

■      - 

/i                             ■■         1 
.1 

t:^     h 

I 


.17.  If  a  body  moves,  it  must  move  eitlier  in  the  place  where 
it  is,  or  in  the  place  where  it  is  not.  liiit  a  body  cannot  move 
in  the  i)lace  where  it  is,  nor  yet  in  the  i)lace  where  it  is  not. 
Hence  a  l)ody  cannot  move  at  aU. 

48.  We  have  no  perfect  idea  (^f  anything  but  a  perception. 
A  substance  is  entirely  different  from  a  perception.  We  have 
therefore  no  idea  of  substance.     (Hume.) 

49.  Iwery  good  government  i)romotes  the  intelligence  of  the 
people,  and  no  (les[)otism  does  that.      (IJain.) 

50.  He  was  too  impulsive  a  man  not  to  have  committed 
many  errors.     (Hain.) 

51.  A  true  philosopher  is  independent  of  the  caprices  of 
fortune,  for  he  places  his  chief  happiness  in  moral  and  intel- 
lectual e.vcellence. 

52.  Educated  among  savages,  he  could  not  be  expected  to 
know  the  customs  of  polite  society,     (liain.) 

53.  No  war  is  long  popular ;  for  every  war  increases  taxa- 
tion, and  the  popularity  of  anything  that  touches  our  pockets 
is  very  short  lived. 

54.  The  general  object  which  all  laws  have,  or  ought  to 
have,  in  common,  is  to  augment  the  total  happiness  of  the 
community  ;  and  therefore,  in  the  fust  place,  to  exclude  as  far 
as  may  be  everything  that  tends  to  subtract  from  that  happi- 
ness :  in  other  words,  to  exchide  mischief.  But  all  punishment 
is  mischief;  all  punishment  in  itself  is  evil.  Upon  the  princi- 
ple of  utility,  if  it  ought  at  all  to  be  admitted,  it  ought  only  to 
be  admitted  in  as  far  as  it  promises  to  exclude  some  greater 
evil.     (Bentham.) 

55.  Experiments  for  the  purpose  of  ascertaining  the  function 
of  the  various  animals  cause  pain,  and  as  we  are  not  warranted 
in  causing  pain  to  any  sentient  creature,  such  experiments  are 
wrong. 

56.  Thou  shalt  not  bear  false  witness  against  thy  neighbour. 


(^UKSIlo.NS    AND    llXKkCISKS 


3(3; 


NSi'f 


the  phicc  whore 
dy  cannot  move 
^vhcrc  it  is  not. 

lilt  a  perception, 
tion.     W'c  have 


telHgcncc  of  the 


have  committed 

the  caprices  of 
iioral  and  intel- 

be  expected  to 

r  increases  taxa- 
hes  our  pockets 

^'e,  or  ought  to 
appiness  of  the 
o  excUide  as  far 
om  that  happi- 
;  all  punishment 
Jpon  the  princi- 
it  ought  only  to 
e  some  greater 

ing  the  function 
e  not  warranted 
experiments  are 


thy 


neighbour. 


57.  What  is  the  use  of  all  this  teaching?  Mvcry  day  you 
hear  of  a  fnrul  or  forgery,  by  some  one  who  might  have  led 
an  innocent  life,  if  he  had  never  learned  to  read  and  write, 
(lulinburgh.) 

58.  Pious  men  only  are  fit  to  be  ministers  of  religion  ;  some 
men  who  have  not  received  a  college  education  are  pious  men, 
therefore  such  men  are  fitted  to  be  ministers  of  religion. 

59.  What  fallacy  did  Columbus  commit  when  he  proved 
that  an  egg  could  stand  on  end?    (Jevons.) 

60.  No  traitor  is  to  be  trusted,  John  is  no  traitor,  and 
therefore  is  to  be  trusted. 

61.  Against  what  fallacy  does  the  proverb,  'all  that  glitters 
is  not  gold,'  warn  us? 

62.  Livy  describes  prodigies  in  his  history,  therefore  he  is 
never  to  be  believed. 

63.  The  theory  of  evolution  is  true,  for  it  is  accepted  by 
every  scientific  biologist. 

64.  The  theory  of  evolution  is  not  true,  for  it  was  not  ac- 
cepted by  Agassiz,  nor  by  (Uadstone  ;  moreover,  you  cannot 
accept  this  doctrine,  for  it  is  disclaimed  by  the  authorities  of 
your  church. 

65.  The  advantages  which  would  accrue  to  the  working- 
classes  are  not  sufficient  to  justify  Protection,  neither  are  the 
advantages  which  it  would  bring  to  the  farmers  or  the  manu- 
facturers, or  to  any  other  class  in  the  community ;  Protection 
therefore  has  not  enough  advantages  to  justify  it. 

66.  No  man  should  be  punished  if  he  is  innocent ;  this  man 
should  not  be  punished ;  therefore  he  is  innocent. 

67.  He  could  not  face  bullets  on  the  field  of  batde,  and  is 
therefore  a  coward. 

68.  We  know  that  God  exists  because  the  Bible  tells  us  so ; 
and  we  know  that  whatever  the  Bible  affirms  must  be  true 
because  it  is  of  divine  origin. 


'M 


.i. 


<}i 


QUESTION'S   AND    KXKKCISKS 

69.  Nations  arc  jtistifiod  in  revolting  when  badly  govcrncil 
for  every  people  has  a  right  to  good  government.    (  Mdinhiirgh.) 

70.  When  ('nesns  was  about  to  make  war  ui)on  ("yrus,  King 
of  Persia,  he  consulted  the  oracle  at  I)el|)hi,  and  received  for 
an  answer  that,  if  he  should  wage  war  against  the  Persians,  he 
would  overthrow  a  mighty  empire. 

71.  I'jigland  has  a  gold  coinage,  and  is  a  very  wealthy  coun- 
try, therefore  it  may  be  inferred  that  other  countries  having  a 
gold  ct)inage  will  be  wealthy. 

72.  Your  arguments  against  the  philosophy  of  Ilegel  are 
of  no  value  ;  for  you  uphold  that  of  Schopenhauer,  which  is 
equally  repugnant  to  common  sense. 

73.  For  those  who  are  bent  on  cultivating  their  minds  by 
diligent  study,  the  incitement  of  academical  honours  is  unnec- 
essary ;  and  it  is  ineffectual  for  the  idle,  and  such  as  are  in- 
different to  mental  improvement ;  therefore  the  incitement  of 
academical  honours  is  either  unnecessary  or  ineffectual. 

74.  Without  order  there  is  no  living  in  public  society,  be- 
cause the  want  thereof  is  the  mother  of  confusion,  whereupon 
division  of  necessity  followeth  ;  and  out  of  division,  destruction. 

75.  If  it  is  always  impossible  not  to  sin,  it  is  always  unjust  to 
punish.  Now  it  is  always  impossible  not  to  sin,  for  all  that  is 
predetermined  is  necessary,  and  all  that  is  foreseen  is  pre- 
determined, and  every  event  is  foreseen.  Hence  it  is  always 
unjust  to  punish.     (Leibniz,  Theodicy.^ 

76.  If  a  gas  is  heated,  its  temperature  rises ;  if  its  tempera- 
ture rises,  its  elastic  force  increases  ;  if  its  elastic  force  increases, 
the  pressure  on  the  walls  of  the  containing  vessel  increases ; 
therefore  if  a  gas  is  heated,  the  pressure  on  the  walls  of  the 
containing  vessel  increases.     (R;iy.) 

77.  The  end  of  human  life  is  either  perfection  or  happi- 
ness ;  death  is  the  end  of  human  life,  therefore  death  is  either 
perfection  or  happiness. 


'W 


iX'KsrioNs  AM)  i;\i;k(.isi:s 


3^>9 


l)a(lly  govcrncil 
t.   ( iMlinburgh.) 
\)(m  ("yrus,  KiiiL,' 
ind  received  for 
the  i'ersians,  Ik; 

ry  wealthy  ronn- 
luntries  having  a 

ly  of  Hegel  are 
ihaucr,  which  is 

their  minds  by 

onours  is  unnec- 

such  as  are  in- 

he  incitement  of 

effectual. 

l)lic  society,  be- 

sion,  whereupon 

iion.  destruction. 

always  unjust  to 

n,  for  all  that  is 

oreseen   is  pre- 

nce  it  is  always 

;  if  its  tempera- 
force  increases, 
essel  increases ; 
the  walls  of  the 

ction  or  happi- 
s  death  is  either 


\ 


M 


7S.  If  light  consisted  of  material  particles,  it  would  possess 
mouunttnn  ;  it  cannot  (  onsist  of  material  particles,  for  it  does 
not  possess  momentum. 

79.  This  pcr.M)!!  is  very  learned,  and  very  sociable,  hence  it 
follows  that  learning  increases  sociabilitv. 

So.  Wliy  advocate  socialism?  Until  men  become  morally 
])erfec:t,  it  is  impossible  ;  when  they  have  become  so,  it  will  be 
unnecessary.     ( I'.dinburgh.) 

81.  The  diameter  of  the  earth  is,  in  round  numbers,  forty 
millions  of  feet.  Consecjuenlly  the  atlraition  of  a  sphere  of  the 
same  mean  density  as  the  earth,  but  one  lo(tt  in  diameter,  will 
1>^"  louii'uoiM,  P^H't  the  attraction  of  the  earth  ;  that  is,  ., „ ,,00 0 ,» 0 
of  the  weigh;  of  the  body  attracted.  Conseipiently,  if  we  should 
measure  the  attraction  of  such  a  sphere  of  lead,  and  find  that 
it  was  just  I „,) o'(M) 0 11  ^'^'^'^  **'  ^^^^  weight  of  the  body  attracted, 
we  would  conclude  that  the  mean  density  of  the  earth  was 
ecjual  to  that  of  lead.  lUil  the  attraction  is  actually  found  to 
be  nearly  twice  as  great  as  this  ;  consequently  a  leaden  sphere 
is  nearly  twice  as  dense  as  the  average  of  the  matter  composing 
the  earth.     (Newcomb,  Pof^ular  Astronomy.) 

(S2.  Mr.  C.  said  that  he  was  certain  that  the  donors  gave  the 
property  to  the  institution  with  a  distinct  and  unanimous 
understanding  as  to  its  future  use.  The  directors  who  acted 
for  the  institution  in  this  transfer  must  necessarily  have  had  an 
understanding,  either  the  same  as  that  of  the  donors,  or  differ- 
ent. If  the  understanding  of  the  directors  was  the  same  as 
that  of  the  donors,  then  they,  the  former,  were  unquestionably 
bound  to  live  up  to  that  understanding.  If  it  was  different, 
then  the  proj^erty  was  conveyed  on  a  misunderstanding,  and 
every  dictate  of  honour  and  fair  play  would  demand  the  return 
of  the  property. 

2B 


f 


i:  < 


li      ii 


4\ 


370  QUESTIONS   AND   EXERCISES 


PART  II. — Inductive   Methods 
Chapter  XIII.  —  T/ic  rroblcin  of  Induction 

1.  Explain  why  syllogistic  logic  is  not  a  complete  account 
of  the  nature  of  thinking. 

2.  In  what  sense  is  it  possible  to  lay  down  the  laws  of  scien- 
tific procedure? 

3.  In  solving  a  com[)lex  scientific  problem  do  we  usually 
employ  but  a  single  method  ? 

4.  What  can  you  say  regarding  the  division  of  inductive 
methods  into  methods  of  Observation,  and  methods  of  Expla- 
nation ? 

5.  Would  it  be  permissible  to  add  Experimental  methods  as 
a  third  and  independent  class? 

6.  What  is  the  distinction  between  '  empirical '  and  '  scien- 
tific '  knowledge  ? 

7.  What  are  the  advantages  to  be  derived  fro  11  experiments 
in  scientific  work  ? 


IB    !    1 

111 


in  IB!"'  I 


Jii 


I  m 


1 


I! 


r 


'1   >   \\       y  '.' 


Chapter  XIV.  —  Enumeration  and  Statistics 

1.  What  is  the  justification  for  beginning  our  account  of  the 
inductive  methods  with  Enumeration? 

2.  Explain  what  Jevons  regards  as  *  Perfect '  induction. 
Has  this  process  any  right  to  the  name? 

3.  For  what  purpose  are  statistics  employed?  To  what 
classes  of  phenomena  are  they  ai)plied? 

4.  What  is  meant  by  a  phenomenon? 

5.  l^xplain  how  statistics  may  suggest  causal  laws,  or  confirm 
our  expectation  of  them.  May  statistics  also  be  used  to  dis- 
prove a  proposed  law  of  causal  connection?  Illustrate  your 
answer. 


sES 

ETHODS 
Induction 
complete  account 

1  the  laws  of  scien- 

em  do  we  usually 

isioii   of  inductive 
aethods  of  ExpUi- 

nental  methods  as 

irical '  and  '  scien- 

fro-n  experiments 

Statistics 

ur  account  of  the 

jrfect '    induction. 

3yed?      To  what 


.1  laws,  or  confirm 

be  used  to  dis- 

Illustrate  your 


(,)UESTIONS   AND    EXERCISES 


17^ 


6.  I^xj)lain  what  is  meant  by  the  *  average,'  and  show  how  it 
is  obtained. 

7.  How  does  the  procedure  of  insurance  companies  differ 
from  gambling? 

Chaiter  XV.  —  Causal  Determination 

1.  What  are  the  two  main  principles  upon  which  the  canons 
proposed  by  Mill  are  founded  ? 

2.  Clive  the  Canon  of  the  Method  of  Agreement,  and  illus- 
trate its  use. 

3.  '  I  have  noticed  that  A  always  precedes  V>,  it  is  there- 
fore the  cause  of  ]].'     Is  this  good  reasoning? 

4.  What  is  meant  by  the  '  Plurality  of  Causes  '  ? 

5.  Under  what  disadvantages  does  the  Method  of  Agreement 
labour?     How  is  it  supplemented? 

6.  State  and  illustrate  the  canon  of  the  Method  of  Differ- 
ence. 

7.  ^Vhy  is  this  method  applicable  only  to  the  spheres  where 
experiment  can  be  employed?  Would  it  be  safe  to  depend 
upon  this  method  in  determining  the  causes  of  social  or  politi- 
cal conditions? 

Chapter  XVI.  —  Causal  Determination   {continued) 

1.  Where  do  we  employ  the  Joint  Method? 

2.  What  would  it  be  necessary  to  establish  in  order  to 
prove  inductively  that  some  change  in  the  tariff  laws  was 
beneficial  to  the  country? 

3.  '  One  of  the  main  characteristics  of  modern  science  is  its 
quantitative  nature.'     Explain. 

4.  Huw  loes  the  law  of  Concomitant  Variations  assist  us  in 
determining  causal  relations  ? 


ill 


/(    ' 


i! 


!  :i=« 


!?      * 


37- 


(^UESTIONS   AND    EXERCISES 


5.  In  what  two  ways  may  the  Method  of  Residues  be 
apphed? 

6.  Mention  some  discoveries  to  which  the  investigation  of 
unexplained  residues  has  led. 

Chai'IKR  XVII. — Analogy 

1.  Why  do  we  include  Analogy  among  the  methods  of  Ex- 
l)lanation? 

2.  What  do  you  mean  by  Analogy?  ^Vhat  is  the  principle 
upon  which  it  proceeds? 

3.  How  is  the  word  used  in  mathematical  reasoning,  and  in 
physiology? 

4.  Into  what  Figure  of  the  Syllogism  does  an  argument 
from  Analogy  naturally  fall  ?  Is  the  argument  formally  valid, 
and  if  not,  to  what  syllogistic  fallacy  does  it  correspond  ? 

5.  Explain  how  Analogy  may  suggest  a  true  law  or  explana- 
tory principle. 

6.  Why  do  we  speak  of  Analogy  as  Incomplete  Explanation? 

7.  If  all  •  ilogical  reasoning  yields  only  probability,  is  not 
one  analogy  -  -  'od  as  another  for  purposes  of  inference?  If 
not,  upon  wi.at  does  the  value  of  an  inference  from  Analogy 
depend  ? 

Chapter  XVIII.  —  The   Use  of  Hypotheses 

1.  How  do  you  distinguish  the  terms  'theory'  and  'hy- 
pothesis '  ? 

2.  What  is  an  hypothesis,  and  how  is  it  used? 

3.  Do  hyi)otheses  play  any  part  in  assisting  Observation? 
Explain  and  illustrate. 

■ '  4.  (live  some  instances  in  which  hypotheses  have  proved 
injurious,  and  have  misled  people  regarding  the  nature  of 
facts. 


.^'\ 


QUESTIONS  AND   EXERCISES 


Liethods  of  Ex- 


373 


5.  'Hypotheses  are  formed  by  the  imagination  working  in 
dependence  upon  facts  and  guided  by  analogy.'     l'A])lain. 

6.  What  are  the  steps  in  the  proof  of  an  hypothesis? 

7.  Explain  what  part  is  played  by  Induction  and  Deduction 
respectively  in  using  hypotheses. 

8.  What  canons  have  been  laid  down  to  which  a  good  hy- 
pothesis must  conform?  Why  are  the  first  and  third  of  these 
rules  of  little  value  ? 

9.  Explain  why  an  unverifiable  hypothesis  is  not  worth  dis- 
cussing. 


Observation? 


Chapter  XIX.  —  Fallacies  of  Induction 

1.  What  is  the  source  of  fallacy?  How  f:ir  is  it  true  that  the 
study  of  Logic  can  protect  us  from  fliUacies? 

2.  How  do  you  classify  Inductive  Fallacies? 

3.  Exi^lain  and  illustrate  the  following  fallacies  :  Qucstion- 
hc^^ing  Epithet,  Equivocation,  Fallacies  due  to  Figurative  Lan- 
guage. 

4.  Explain  and  illustrate  the  tendency  of  the  mind  to  neg- 
lect negative  cases. 

5.  Is  it  an  easy  matter  to  *  tell  just  what  we  saw  and  heard  ' 
at  a  particular  time  ? 

6.  Wliat  do  you  mean  by  post  hoc  ergo  propter  hoc  ?  Why 
may  we  take  this  as  the  general  type  of  inductive  fallacies? 

7.  What  did  Bacon  mean  by  the  Idols  of  the  Cave? 

8.  *  Every  age,  as  well  as  every  individual,  has  its  idols.' 
Explain  this    statement. 

]\[lSCET,T,ANF.OUS    EXAMPLES 

Analyze  the  examples  of  inductive  reasoning  given  below, 
and  point  out  what  methods  are  employed,  indicating  also 
whether  or  not  the  conclusion  is  completely  established :  — 


^'^T'f^^i'fimsii 


374 


OUESTIOXS   AND    EXERCISES 


1.  In  my  experience  A  has  been  invariably  preceded  by  B, 
and  we  may  therefore  conclude  that  it  is  the  cause  of  it. 

2.  Scarlet  poppies,  scarlet  verbenas,  the  scarlet  hawthorn, 
and  honeysuckle  are  all  odourless,  therefore  we  may  conclude 
that  all  scarlet  flowers  are  destitute  of  odour. 

3.  What  inference,  if  any,  can  be  drawn  from  the  follow- 
ing statement :  '  In  nine  counties,  in  which  the  population 
is  from  100  to  150  per  sc^uare  mile,  the  births  are  296 
to  [oo  marriages  ;  in  sixteen  counties,  with  a  population 
of  150  to  200  per  square  mile,  the  births  are  308  to  100 
marriages  '  ? 

4.  The  great  famine  in  Ireland  began  in  1845  ^^'^^  reached 
its  climax  in  1848.  During  this  time  agrarian  crime  increased 
very  rapidly,  until,  in  1848,  it  was  more  than  three  times  as 
great  as  in  1845.  After  this  time  it  decreased  with  the  return 
of  better  crops,  un''l,  in  185 1,  it  was  only  50  per  cent  more  than 
it  was  in  1845.  It  is  evident  from  this  that  a  close  relation 
of  cause  and  effect  exists  between  famine  and  agrarian  crime. 
(Hyslop.) 

5.  Sachs  maintained,  in  1862,  that  starch  is  formed  by  the 
decomposition  in  chlorophyl  of  carbon-dioxide  gas  under  the 
influence  of  light.  He  found  that  when  all  other  conditions 
were  constant,  and  light  was  excluded  from  a  plant,  no  starch 
was  formed  ;  the  single  circumstance  of  readmitting  light  was 
accompanied  by  renewed  formation  of  starch.  Further,  he 
found  that  if  certain  portions  of  the  leaves  of  an  illuminated 
plant  were  covered  with  black  paper,  no  starch  was  found  in 
these  portions. 

6.  Jupiter  gives  out  more  light  than  it  receives  from  the  sun. 
What  is  the  obvious  conclusion,  and  by  what  method  is  it 
reached  ? 

7.  What  methods  would  you  employ  in  order  to  test  the 
truth  of  the  proposition,  omne  vivuin  ex  ovo  ? 


\  ^ 


^receded  by  B, 
use  of  it. 
arlet  hawthorn, 
;  may  conclude 

:om  the  follow- 
the  population 
births  are  296 
h  a  population 
ire   308  to   100 

;45  and  reached 
crime  increased 
I  three  times  as 
I  with  the  return 
r  cent  more  than 
a  close  relation 
i  agrarian  crime. 

formed  by  the 

e  gas  under  the 

other  conditions 

plant,  no  starch 

mitting  hght  was 

Further,  he 

f  an  illuminated 

ch  was  found  in 

^es  from  the  sun. 
at  method  is  it 

)rder  to  test  the 


s^n 


QUESTIONS   AND    EXERCISES 


375 


8.  War  is  a  blessing,  not  an  evil.  Show  me  a  nation  that 
has  ever  become  great  without  blood-letting. 

9.  If  wages  de[)end  upon  the  ratio  between  the  amount  of 
labor-seeking  employment,  and  the  amount  of  cai)ital  devoted 
to  its  employment,  the  relative  scarcity  or  abundance  of  one 
flictor  must  mean  the  relative  abundance  or  scarcity  of  the 
other.  Thus  capital  must  be  relatively  abundant  where  wages 
are  high,  and  relatively  scarce  where  wages  are  low.  Now,  as 
the  capital  used  in  paying  wages  must  largely  consist  of  the 
capital-seeking  investment,  the  current  rate  of  interest  must  be 
the  measure  of  its  relative  abundance  or  scarcity.  So  if  it  be 
true  that  wages  depend  upon  the  ratio  between  the  amount  of 
labor-seeking  employment,  and  the  capital  devoted  to  its  em- 
ployment, then  high  wages  must  be  accompanied  by  low  inter- 
est, and,  reversely,  low  wages  must  be  accompanied  by  iiigh 
interest.     This  is  not  the  fact  but  the  contrary,     ((ieorge.) 

10.  Construct  an  inductive  argument  to  prove  that  some 
article  of  food,  or  some  habit,  is  beneficial  or  injurious  to  you, 
and  analyze  your  reasoning,  showing  the  methods  which  you 
have  employed. 

11.  Some  comets  have  been  observed  to  have  the  same 
orbits  as  certain  meteoric  showers.  The  hypothesis  is  suggested 
that  all  meteoric  showers  may  represent  the  dc'bris  of  disinte- 
grated showers.  Biela's  comet  having  been  missing  for  some 
time,  it  was  accordingly  predicted  that  when  next  due  it  would 
be  replaced  by  a  meteoric  shower.  This  prediction  was  verified 
by  observation. 

12.  Lyndall  found  that  of  twenty-seven  sterilized  flasks  con- 
taining infusion  of  organic  matter,  and  opened  in  pure  Alpine 
air,  not  one  showed  putrefaction  ;  while  of  twenty-three  similar 
flasks,  opened  in  a  hay-loft,  only  two  remained  free  from  putre- 
faction after  three  days.  He  concluded  that  putrefaction  is 
due  to  floating  particles  in  the  air. 


|i 


h     Wi 


37^^ 


QUKSTIOXS   AND    KXKR(;:iSES 


», 


M^  •■'^ 


it 


1; 


13.  'Whether  or  not  a  bad  theory  is  Inciter  than  none, 
(le|)en(ls  upon  cireunistances.'  Examine  this  statement,  and 
point  out  what  are  some  of  the  circumstances  of  which  mention 
is  made. 

14.  It  is  saiii  that  a  general  resemblance  of  the  hills  near 
]>allarat  in  Australia  to  the  Californian  hills  where  gold  had 
been  found  suggested  the  idea  of  digging  for  gold  at  IJallarat. 
(Minto.) 

15.  There  are  no  great  nations  of  anticpiity  but  ha\'e  fallen 
to  the  hand  of  time ;  and  I'^ngland  must  join  them  to  complete 
the  analogy  of  the  ages.  Like  them  she  has  grown  from  a 
birth-time  of  weakness  and  tutelage  to  a  day  of  manhood  and 
supremacy  ;  but  she  has  to  face  her  setting.  Everything  that 
grows  must  also  decay.     (Edinburgh,  1S93.) 

16.  Cioldscheider  proved  that  muscular  sensations  play  no 
considerable  part  in  our  consciousness  of  the  movements  of  our 
limbs,  by  having  his  arm  suspended  in  a  frame  and  moved  by 
an  attendant.  Under  these  circumstances,  where  no  work 
devolved  on  his  muscles,  he  found  that  he  could  distinguish  as 
small  an  angular  movement  of  the  arm  as  when  he  moved  and 
supported  it  himself. 

17.  Goldscheider  also  proved  that  the  chief  source  of  move- 
ment-consciousness is  pressure  sensations  from  the  inner  sur- 
face of  the  joints,  by  having  his  arm  held  so  that  the  joint 
surfaces  were  pressed  more  closely  together,  and  finding  that 
a  smaller  movement  was  now  perceptible. 

18.  Wages  in  the  United  States  are  higher  than  in  England, 
because  the  former  country  is  a  republic  and  has  a  protective 
tariff. 

19.  It  does  not  follow  that  an  institution  is  good  because  a 
country  has  prospered  under  it,  nor  bad  because  a  country  in 
which  it  exists  is  not  prosperous.  It  does  not  even  follow  that 
institutions  to  be  found  in  all  prosperous  countries,  and  not 


■   f| 


QUESTIONS   AND    IIXKRCISES 


377 


er  than  none, 
itatemcnt,  and 
which  mention 

the  hills  near 
lere  gold  had 
Ad  at  Ballarat. 

but  have  fallen 

n\  to  complete 

grown  from  a 

manhood  and 

everything  that 

ations  play  no 
vements  of  our 
and  moved  by 
here  no  work 
1  distinguish  as 
he  moved  and 

)urce  of  move- 
the  inner  sur- 
>  that  the  joint 
1   finding  that 

m  in  England, 
IS  a  protective 

Dod  because  a 

e  a  country  in 

en  follow  that 

tries,  and  not 


to  be  found  in  backward  coimtries,  arc  therefore  beneficial. 
For  this  at  various  times  might  confidently  ha\c  been  asserted 
of  slavery,  of  polygamy,  of  aristocracy,  of  established  churches  ; 
and  it  may  still  be  asserted  of  public  debts,  of  private  i)roperty 
in  land,  of  pauperism,  and  of  the  existence  of  distinctly  vicious 
or  criminal  classes,     ((leorge.) 

20.  I'lxplain  the  procedure  of  the  rcdnciio  ad  al'sinJii/ii  form 
of  argument. 

21.  It  may  be  a  coincidence  merely;  but,  if  so,  it  is  re- 
markably strange  that  while  the  chloroform  has  not  changed, 
while  the  constitutions  of  the  patients  have  not  changed,  where 
the  use  of  the  inhaler  is  the  rule  there  are  frccpient  deaths  from 
chloroform  ;  whilst  in  Scotland  and  Ireland,  where  the  use  of 
the  inhaler  is  the  exception,  deaths  are  jiroportionally  rare. 

2  2.  We  should  think  it  a  sin  and  shame  if  a  great  steamer, 
dashing  across  the  ocean,  were  not  brought  to  a  stop  at  a  signal 
of  distress  from  the  mere  smack.  .  .  .  And  yet  a  miner  is 
entombed  alive,  a  painter  falls  from  a  scaffold,  a  brakeman  is 
crushed  in  coupling  cars,  a  merchant  fails,  fells  ill  and  dies,  and 
organized  society  leaves  widow  and  child  to  bitter  want  or 
degrading  alms.     (George.  Protection  and  Free  Trade.) 

23.  Manufacturing  '  ountries  are  always  rich  countries; 
countries  that  ]:)roducc  raw  material  are  always  poor.  There- 
fore, if  we  would  be  rich,  we  must  have  manufactures,  and  in 
order  to  get  them,  we  must  encourage  them.  .  .  .  l>ut  I  could 
make  as  good  an  argument  to  the  little  town  of  Jamaica  .  .  . 
in  support  of  a  subsidy  to  a  theatre,  I  could  say  to  them  :  all 
cities  have  theatres,  and  the  more  theatres  it  has  the  larger  the 
city.  Look  at  New  York  !  .  .  .  Philadelphia  ranks  next  to 
New  York  in  the  number  and  size  of  its  theatres,  and  therefore 
comes  next  to  New  York  in  wealth  and  population.  ...  I 
might  then  drop  into  statistics  .  .  .  auvl  jioint  to  the  fact  that 
when  theatrical  representations  began  in  this  country,  its  popu- 


37« 


OUKSTIOXS    AND    EXI'RC'ISES 


I  •'  I 


m 


;]l 


hition  did  not  amount  to  a  million,  that  it  was  totally  destitute 
of  railroads,  and  without  a  single  mile  of  telegra[)h  wire.  Such 
has  been  our  progress  since  theatres  were  introduced  that  the 
census  of  18S0  showed  we  had  5",  155,783  people,  90,907  miles 
of  railroad,  and  291,212,",^  miles  of  telegraph  wires.  (George, 
Protection  and  Free  7'fattc\) 

24.  What  methods  would  you  employ  to  investigate  the  con- 
nection between  changes  in  the  barometer  and  in  the  weather  ? 

25.  In  Sir  Hum[)hry  J)avy's  experiments  upon  the  decom- 
position of  water  by  galvanism,  it  was  found  that,  besides 
the  two  components  of  water,  oxygen  and  hydrogen,  an  acid 
and  an  alkali  were  developed  at  the  two  opposite  poles  of  the 
machine.  The  insight  of  Davy  conjectured  that  there  might 
be  some  hidden  cause  of  this  portion  of  the  effect :  the  glass 
containing  the  water  might  suffer  partial  decomposition,  or 
some  foreign  matter  might  be  mingled  with  th(>  water,  and  the 
acid  and  alkali  be  disengaged  from  it,  so  that  the  water  would 
have  no  share  in  their  production.  ...  By  the  substitution  of 
gold  vessels  for  glass,  without  any  change  in  the  effect,  he  at 
once  determined  that  the  glass  was  not  the  cause.  Employing 
distilled  water,  he  found  a  marked  diminution  of  the  quantity 
of  acid  and  alkali  evolved  ;  yet  there  was  enough  to  show  that 
the  cause,  whatever  it  was,  was  still  in  operation.  .  .  .  He 
now  conceived  that  the  perspiration  from  the  hands  touching 
the  instruments  might  affect  the  case,  as  it  would  contain 
common  salt,  and  an  acid  and  an  alkali  would  result  from  its 
decomposition  under  the  agency  of  electricity.  By  carefully 
avoiding  such  contact,  he  reduced  the  quantity  of  the  products 
still  further  until  no  more  than  slight  traces  of  them  were  per- 
ceptible. An  experiment  determined  this  :  the  machine  was 
put  under  an  exhausted  receiver,  and  when  thus  secured  from 
atmospheric  influence,  it  no  longer  evolved  the  acid  and  the 
alkali.     (Gore,  The  Art  of  Scientific  Discovery?) 


n 


\l\ 


\v^ 


QUESTIONS    AM)    KXHRCTSKS 


379 


3tally  destitute 
»h  wire.  Such 
uccd  that  the 
i,  90,907  miles 
cs.      (George, 

tigate  the  con- 
1  the  weather  ? 
3n  the  decom- 
[    that,  besides 
.rogen,  an  acid 
;e  poles  of  the 
at  there  might 
feet :  the  glass 
:omposition,  or 
water,  and  the 
le  water  would 
substitution  of 
e  effect,  he  at 
Employing 
'  the  quantity 

1  to  show  that 
ion.  .  .  .  He 
lands  touching 
would  contain 
result  from  its 

By  carefully 
3f  the  products 
lem  were  per- 

2  machine  was 
secured  from 
acid  and  the 


26.  Properties  known  to  exist  in  potassium  have  been  pre- 
dicted of  and  found  to  exist  in  rubidium  ;  for  instance,  the 
carbonates  of  sodium  and  potassium  are  not  decomposed  by 
a  red  heat,  neither  are  those  of  rubidium,  or  ci\3sium.  Some 
of  the  statements  which  are  true  of  chlorine  have  been  found  to 
be  true,  in  varying  degrees,  of  bromine  and  iodine.  .  .  .  After 
1  had  found  the  molecular  change  in  antinomy  electo-deposited 
from  its  chloride,  I  souglit  for  and  discovered  it  in  that  de- 
posited from  its  bromide  and  iodide  ;  and  after  having  found 
magnetic  changes  in  iron  by  heat,  I  also  found  similar  ones  in 
nickel,      ((iore,  llie  Art  of  Sciciitijic  Discoirry.) 

27.  What  indu.  .ive  fallacy  may  David  be  said  to  have 
committed  wlien  he  said  in  his  haste  that  all  men  are  liars.'' 

28.  It  has  been  found  that  linnets  when  shut  up  and  edu- 
cated with  singing  larks  —  the  skylark,  woodlark,  or  titlark  — 
will  adhere  entirely  to  the  songs  of  these  larks,  instead  of  the 
natural  song  of  the  linnets.  We  may  infer,  therefore,  that 
birds  learn  to  sing  by  imitation,  and  that  their  songs  are  no 
more  innate  than  language  is  in  man.     (Hyslop.) 

29.  We  observe  very  frequently  that  very  poor  handwriting 
characterizes  the  manuscripts  of  able  men,  while  the  best  hand- 
writing is  as  frequent  with  those  who  do  little  mental  work 
when  compared  with  those  whose  penmanshij)  is  poor.  We 
may,  therefore,  infer  that  poor  penmanship  is  caused  by  the 
influence  of  severe  mental  labor.     (Hyslop.) 

30.  Galileo  describes  his  invention  of  the  telescope  as  fol- 
lows :  This  then  was  my  reasoning ;  this  instrument  [of 
which  he  had  heard  a  rumor]  must  either  consist  of  one  glass, 
or  of  more  than  one  ;  it  cannot  be  of  one  alone,  because  its 
figure  must  be  either  concave  or  convex,  or  comprised  within 
two  parallel  superficies,  but  neither  of  these  shapes  alter  in  the 
least  the  objects  seen,  although  increasing  or  diminishing  them  ; 
for  it  is  true  that  the  concave  glass  diminishes,  and  that  the 


■■''!'■ '  i 


i     < 


380 


QUESTIONS   AXI)    KXHRCISES 


convex  glass  increases  them  ;  but  both  show  them  very  indis- 
tinctly, and  hence  one  glass  is  not  sufficient  to  produce  the 
efifect.  Passing  on  to  two  glasses,  and  knowing  that  the  glass 
of  parallel  superficies  has  no  effect  at  all,  I  concluded  that  the 
desired  result  could  not  possibly  follow  by  adding  this  one  to 
the  other  two.  I  therefore  restricted  my  experiments  to  com- 
binations of  the  other  two  glasses  ;  and  1  saw  how  this  brought 
me  to  the  result  I  desired.  ((Quoted  by  (lore,  T/ic  A?-f  of  Scien- 
tific Discovery.^ 

31.  Darwin  was  struck  by  the  number  of  insects  caught  by 
the  leaves  of  the  common  sun-dew.  It  soon  became  evident 
to  him  that  "  Drosera  was  excellently  adai)tcd  for  the  special 
purpose  of  catching  insects."  ...  As  soon  as  he  began  to 
work  on  Drosera,  and  was  led  to  believe  that  the  leaves  ab- 
sorbed nutritious  matter  from  the  insects,  he  began  to  reason 
by  analogy  from  the  well-understood  digestive  capacity  of  ani- 
mals. .  .  .  Having  by  analogy  established,  the  power  of  di- 
gestion in  plants,  analogy  led  him  to  seek  in  plants  the  elements 
that  do  the  work  of  digestion  in  animals.  IJringing  together 
what  was  known  of  plants,  he  pointed  out  that  the  juices  of 
many  plants  contain  an  acid,  and  so  one  element  of  a  digestive 
fluid  was  at  hand  ;  and  that  all  plants  possess  the  power  of 
dissolving  albuminous  or  proteid  substances,  protoplasm,  chlo- 
rophyl,  etc.,  and  that  "  this  must  be  effected  by  a  solvent,  proba- 
bly consisting  of  ferment  together  with  an  acid."  After  writing 
the  last-quoted  sentence,  he  learned  that  a  ferment  which  con- 
verted albuminous  substances  into  true  peptones  had  been 
extracted  from  the  seeds  of  the  vetch.  (Cramer,  The  Method 
of  Darwin.^ 

32.  Strongly  impressed  with  the  belief  that  some  *  harmonic  ' 
relation  must  exist  among  the  distances  of  the  several  planets 
from  the  sun,  and  also  among  the  times  of  their  revolution, 
Kepler  passed  a  large  part  of  his  early  life  in  working  out  a 


()Ui:sri()NS   AND    KXKIUISKS 


3«' 


scries  of  }^i/esscs  at  this  relation,  some  of  which  now  strike  us 
as  not  merely  most  impn^ixible,  but  positively  ridiculous.  His 
single-mindeil  devotion  to  truth,  however,  leil  him  to  abandon 
each  of  these  hy|)otheses  in  turn  so  soon  as  he  perceived  its 
fallacy  by  submitting  it  to  the  test  of  its  conformity  to  observed 
facts.  .  .  .  Hut  he  was  at  last  rewarded  by  the  discovery  of 
that  relation  between  the  times  and  the  distances  of  the  |)Ianet- 
ary  revolutions,  which  with  the  discovery  of  the  ellipticity  of  the 
Dibits,  and  of  the  j)assage  of  the  radius  ve(  tor  over  equal  areas 
ill  equal  li/nes  has  giveji  him  in^mortality  as  an  astronomical 
discoverer.  JJut  ...  he  was  so  far  from  divininu;  the  true 
rationale  of  the  j^lanetary  revolutions  that  he  was  led  to  the 
discovery  of  the  elliptical  orbit  of  Mars  by  a  series  of  hai)py 
accidents  .  .  .  whilst  his  discovery  of  the  true  relations  of 
times  and  distances  was  the  fortunate  guess  which  closed  a 
long  series  of  //-//fortunate  ones,  many  of  which  were  no  less 


ingenious. 


Now  it  was  by  a  grand  effort  of  Newton's  construetive  imagi- 
nation, based  on  his  wonderful  mastery  of  geometrical  reason- 
ing, that,  starting  with  the  concei)tion  of  two  forces,  one  of 
them  tending  to  produce  continuous  uniform  motion  in  a 
straight  line,  the  other  tending  to  produce  a  uniformly  acceler- 
ated motion  towards  a  fixed  point,  he  was  able  to  show  that  if 
these  ^/r;/(j;;;//Vv7/ assumptions  were  granted,  Kepler's  laws,  being 
consequences  of  them,  must  be  universally  true.  And  it  was 
his  still  greater  glory  to  divine  the  profound  truth  that  the  fall 
of  the  moon  towards  the  earth  —  that  is  the  deflection  of  her 
path  from  a  tangential  line  to  an  ellipse  —  is  a  phenomenon  of 
the  same  order  as  the  fall  of  a  stone  to  the  ground.  (Gore,  The 
Art  of  Scientific  Discovery.) 

33.  After  Franklin  had  investigated  the  nature  of  electricity 
for  some  time,  he  began  to  consider  how  many  of  the  effects 
of  thunder  and  lightning  were  the  same  as  those  produced  by 


<   J 


382 


nur:sri(A's  and  kxkkcisks 


':  il; 


IM 


t  ■! , 


electricity.  Lipihtiiin,','  travels  in  :i  zif,'-zag  line,  and  so  does  an 
electric  spark  ;  electricity  sets  things  on  fire,  so  does  lightning  ; 
electricity  molts  metals,  so  does  lightning.  Animals  can  be 
killed  by  both,  and  both  cause  blindness.  Pointed  bodies 
attract  the  electric  spark,  and  in  the  same  way  lightning  strikes 
spires,  and  trees,  and  mountain  tops.  Is  it  not  likely  then  that 
lightning  is  nothing  more  than  electricity  passing  from  one 
cloud  to  another,  just  as  an  electric  spark  passes  from  one  sub- 
stance to  another  ?  (Hucklcy,  //  Short  J  lis  to  ry  of  Natural 
Science.) 

34.  How  did  Franklin  proceed  to  verify  the  hyi)othebis 
stated  in  the  last  exam|)le  ? 

35.  (lalileo  discovered  by  means  of  his  telescope  that  Jupi- 
ter has  four  moons,  instead  of  one  like  the  earth,  and  he 
regarded  this  discovery  as  a  confirmation  of  the  Copernican 
theory.  I'^xplain  the  nature  of  the  reasoning  involved  in 
reaching  this  conclusion. 

36.  That  the  period  of  tide  should  be  accidentally  the  same 
as  that  of  the  culmination  of  the  moon,  that  the  period  of  the 
highest  tide  should  be  accidentally  the  same  as  the  syzygies,  is 
possible  /';/  abstracto ;  but  it  is  in  the  highest  degree  improb- 
able :  the  far  more  probable  assumjJtion  is,  either  that  the  sun 
and  moon  produce  the  tide,  or  that  their  motion  is  due  to  the 
same  grounds  as  the  motion  of  the  tide.     (Hibben.) 

37.  During  the  retreat  of  the  Ten  Thousand  a  cutting  north 
wind  blew  in  the  faces  of  the  soldiers,  sacrifices  were  offered 
to  Boreas,  and  the  severity  of  the  wind  immediately  ceased, 
which  seemed  a  proof  of  the  god's  causation.     (Hibben.) 

2^^.  A  nectary  implies  nectar,  but  Sprengel  had  come  to  the 
conclusion  that  orchis  morio  and  orchis  maculafa^  though  fur- 
nished with  nectaries,  did  not  secrete  nectar.  1  )arwin  examined 
the  flowers  of  orchis  morio  for  twenty-three  consecutive  days, 
looking  at  them  after  hot  sunshine,  after  rain,  and  at  all  hours ; 


()Ui:sri()\S   AND    KXKKCISKS 


38j 


and  so  does  an 

does  lightning  j 
minials  can  be 
Pointed  Inxlies 
ightning  strikes 
likely  then  that 
ising  from  one 
s  from  one  sub- 
■jry  of  Natural 

the   hypothesis 

icope  that  Jupi- 

earth,  and   he 

the  Copernican 

ng   involved   in 

intally  the  same 
le  period  of  the 
;  the  syzygies,  is 
degree  improb- 
ler  that  the  sun 
on  is  due  to  the 
jen.) 

a  cutting  north 
es  were  offered 
^diately  ceased, 
(Hibben.) 
ad  come  to  the 
a  fa,  though  fur- 
arwin  examined 
)nsecutive  days, 
nd  at  all  hours  ; 


he  kc])t  the  spikes  in  water  and  examined  them  at  midnight 
and  early  the  next  mornini;.  ilo  irritateil  the  nectaries  with 
bristles,  anil  exposed  them  to  irritating  vapors.  He  examined 
flowers  whose  pollinia  hid  been  removed,  and  others  which 
woulil  i)robal)ly  have  them  scjon  removed.  lUit  the  nectary 
was  invariably  dry. 

Me  was  thoroughly  convinced,  however,  that  these  orchids 
require  the  visits  of  insects  for  fertilization,  and  that  insects 
visit  n(jwers  for  the  attractions  offered  in  the  way  of  nectar,  and 
yet  that  in  these  orchids  the  ordinary  attraction  was  absent. 
In  examining  the  orchids  he  was  surprised  at  the  degree  to 
which  the  inner  and  outer  membranes  forming  the  tube  or 
si)ur  were  sei)arate(l  from  each  other,  also  at  the  delicate  nature 
of  the  inner  membrane,  and  the  ([uantity  of  fluid  contained 
between  the  two  membranes.  I  le  then  examined  other  forms 
that  do  secrete  nectar  in  the  ordinary  way,  and  found  tlie  mem- 
branes closely  united,  instead  of  separated  by  a  space.  '•  I  was 
therefore  led  to  conclude,"  he  says,  *'  that  insects  penetrate  the 
lax  membrane  of  the  nectaries  of  the  above-named  orchids  and 
suck  the  copious  fluid  between  the  two  membranes."  He 
afterwards  learned  that  at  the  Cape  of  (iood  Hope  moths  and 
butterflies  penetrate  peaches  and  plums,  and  in  Queensland  a 
moth  penetrates  the  rind  of  the  orange.  These  facts  merely 
proved  his  anticipation  less  anomalous  than  it  had  seemed. 
(Cramer,  T/tc  Method  of  Darwin.) 

39.  Construct  an  hypothesis  to  ex])lain  some  fact  of  your 
experience,  and  ex})lain  how  it  may  be  either  verified  or  over- 
thrown. 

40.  \Mien  Darwin  began  to  work  on  Drosera  he  was  led 
to  believe  that  the  leaves  absorbed  nutritious  matter  from 
insects.  He  then  reasoned  by  analogy  from  the  well-under- 
stood digestive  capacity  of  animals.  He  made  preliminary 
*  crucial '  experiments  by  immersing  some  leaves  of  Drosera 


384 


QUESTIONS   AND    EXERCISES 


1 

« 

ii 

1! 

1 

'H 

if 


,;S 


in  nitrogeneous  and  others  in  non-nitrogencoiis  fluids  of  the 
same  density  to  determine  whether  the  former  affected  the 
leaves  differently  from  the  latter.  This  he  found  to  be  the  case. 
He  then  experimented  with  solid  animal  matter  and  found 
that  the  leaves  are  capable  of  true  digestion.  Analogy  then 
led  him  to  seek  in  plants  the  elements  that  do  the  work  of 
digestion  in  animals.  He  pointed  out  that  the  juices  of  many 
plants  contain  an  acid,  and  so  one  element  of  a  digestive  fluid 
was  at  hand  ;  and  that  all  plants  possess  the  power  of  dissolving 
albuminous  or  proteid  substance-protoplasm,  chlorophyl,  and 
that  this  must  be  effected  by  a  solvent  consisting  probably 
of  a  ferment  together  with  an  acid.  Afterwards  he  learned 
that  a  ferment  which  converted  albuminous  substances  into 
true  peptones  had  been  extracted  from  the  seeds  of  the  vetch. 
(Cramer,  T/w  Method  of  Dai-win,  pp.  95-99.) 

41.  In  opposition  to  the  facts  stated  above,  Tischutkin 
maintains  that  the  '  digestion '  of  insectivorous  plants  is  not 
accomplished  in  the  same  way  as  in  animals,  but  is  due  to  a 
bacteria  :  that  the  pepsin  is  not  a  secretion  of  the  plant,  but 
a  by-product  of  the  activity  of  the  bacteria.  Suppose  that  this 
theory  is  true,  and  Darwin's  false,  what  would  you  say  regard- 
ing the  character  of  the  latter's  reasoning  ? 

PART   III. — The  Nature  of  Thought 


Chapter  XX.  — Judgment  the  Elementary  Process 

1.  What  objections  are  there  to  speaking  of  thought  as  'a 
thing  like  other  things  '  ? 

2.  What  is  the  general  law  of  Evolution?  Explain  what  is 
meant  by  a  change  from  the  homogeneous  to  the  heterogene- 
ous. 

3.  What  general  conclusions  are  reached  by  the  application 
of  the  law  of  Evolution  to  the  thought-process  ? 


QUESTIONS   AND   KXERCISES 


85 


HOUGHT 


4.  What  do  you  understand  by  Judgment?  How  does  a 
simple  judgment  differ  from  sensation? 

5.  In  what  sense  may  our  judgments  be  said  to  be  the  union 
of  two  concepts  ? 

6.  Would  the  doctrine  that  in  knowing  we  first  have  Simple 
Apprehension,  then  as  separate  intellectual  processes,  Judgment 
and  finally  Inference,  agree  with  the  general  evolutionary  view 
of  consciousness  ?     Tlxplain  fully. 

Chaptkr  XXI.  —  The  Characteristics  of  Judgment 

1.  What  do  you  understand  by  the  universality  of  judg- 
ments ?  What  is  the  distinction  between  the  universality  of  a 
judgment  and  that  of  a  proposition  ? 

2.  How  would  you  prove  that  all  judgments  are  universal? 

3.  Is  any  judgment  necessary  in  itself?  If  not,  whence  do 
judgments  derive  their  necessity? 

4.  What  is  the  argument  by  which  it  has  been  maintained 
that  there  must  be  judgments  or  principles  which  are  in  them- 
selves necessary? 

5.  Explain  how  it  is  possible  for  a  judgment  to  be  at  once 
both  analytic  and  synthetic. 

6.  Explain  what  is  meant  by  a  '  system  '  of  knowledge. 

7.  When  judgment  brings  new  facts  into  relation  to  what 
we  already  know,  does  the  old  body  of  knowledge  undergo  any 
modification  ? 


Explain  what  is 


/  the  application 


Chaiter  XXII.  —  The  Laivs  of  Thought 

1.  In  what  sense  can  we  speak  of  a  law  of  Thought? 

2.  L^xplain  what  is  meant  by  the  law  of  Identity. 

3.  How  has  this  law  been  interpreted  by  Boole  and  Jevons? 

4.  What  does  Jevons  mean  by  the  'substitution  of  similars,' 
and  how  does  he  propose  to  employ  this  principle  ? 

2C 


r 


I 


r-:lH    li; 


!  I 


II 


',>:!'* 


i ;  i        M 

il        i 


*f 


it:!    : 


386 


QUESTIONS   AND   EXICRCISES 


5.  What  objections  are  there  to  employing  the  sign  of 
equality  to  represent  the  relation  between  the  subject  and 
predicate  of  a  judgment? 

6.  Explain  how  the  law  of  Identity  is  related  to  the  charac- 
teristics of  judgment  treated  in  the  last  chapter. 

7.  What  is  the  meaning  of  the  law  of  Contradiction? 

8.  Explain  the  use  of  the  law  of  Excluded  Middle. 

Chapter  XXIII. —  Tv/>es  of  Judgmejit 

1.  Why  do  we  begin  with  judgments  of  Quality? 

2.  Explain  how  we  pass  in  the  development  of  intelligence 
from  Quality  to  Quantity. 

3.  In  what  sense  is  it  true  that  judgments  of  Quantity  never 
give  us  the  real  nature  of  things,  but  only  their  relation  to 
something  else? 

4.  What  is  meant  by  anthropomorphic  causes?  How  are 
they  distinguished  from  scientific  causes? 

5.  What  new  element  did  the  discovery  of  the  law  of  the 
Conservation  of  Energy  introduce  in  the  causal  conception  as 
employed  in  certain  sciences? 

6.  Why  cannot  this  new  extension  have  any  application  in 
the  field  of  the  mental  sciences? 

7.  How  does  the  standpoint  of  judgments  of  Individuality 
differ  from  that  of  judgments  of  Causality? 

Chapter  XXIV.  —  Lifcrence 

1.  How  does  Inference  differ  from  Judgment?  In  what 
sense  may  it  be  said  that  it  is  an  extension  of  the  latter  pro- 
cess? 

2.  Does  the  passage  from  Judgment  to  Inference  illustrate 
the  general  law  of  Logical  Evolution?     Explain. 


ing   the   sign  of 
the  subject  and 

sd  to  the  charac- 

r. 

adiction? 

Middle. 

"■ment 

ality? 

nt  of  intelligence 

)f  Quantity  never 
their  relation  to 

uses?     How  are 

)f  the  law  of  the 
.sal  conception  as 

ny  application  in 

)  of  Individuality 


;ment?     In  what 
of  the  latter  pro- 

nference  illustrate 
)lain. 


QUESTIONS   AND    EXERCISES 


387 


3.  In  the  development  of  our  knowledge,  which  usually 
conies  first,  premises  or  conclusion? 

4.  How  is  it  possible  to  pass  from  the  known  to  the  un- 
known ? 

5.  Explain  under  what  circumstances  only  an  Inference  is 
possible. 

6.  What  is  the  common  element  in  both  Induction  and 
Deduction?     How  do  they  differ? 

Chapter  XXV.--  Rational  and  Empirical  Theories 

1.  Who  are  the  great  historical  representatives  respectively 
of  Rationalism  and  Empiricism? 

2.  Explain  the  method  and  procedure  of  Rationalism. 

3.  What  is  the  great  instrument  of  knowledge  according  to 
Rationalism?     What  according  to  Empiricism? 

4.  State  as  clearly  as  you  can  the  various  points  at  issue 
between  the  two  schools. 

5.  Explain  LJll's  theory  that  we  always  reason  from  one 
particular  fact  to  another.  How  far  do  you  agree  with  his 
conclusions? 

6.  Is  it  true  that  we  obtain  a  general  law  by  summing  up 
particulai  s  ? 

7.  Is  there  any  direct  and  necessary  connection  between  the 
number  of  instances  and  the  induction  of  the  general  law? 

8.  Criticise  Jevon's  theory  of  '  Perfect  Induction '  as  stated 
on  page  187. 


I    J 


■i! 


'/! 


INDEX 


Abstract,  two  Meanings  of  the  Word, 
51- 

Accent,  the  Fallacies  of,  156. 

Accident,  the  Fallacy  of,  163. 

Agreement,  the  Method  of,  200;  De- 
ficiencies in  the  Method  of,  204. 

Amphiboly,  the  Fallacy  of,  156, 

Analogy,  Explanation  by  Means  of, 
219;  the  Principle  of,  221;  Mill's 
Statement  of,  222;  its  Function  in 
suggesting  Hypothesis,  223;  its  Use 
by  Darwin,  225;  its  Incompleteness 
as  a  Method  of  Explanation,  226. 

Analysis,  its  Relation  to  Synthesis,  279. 

Anthropomorphism,  309. 

Apprehension,  Simple,  44. 

A  priori  Truths,  278. 

Arguiiiciitum,  ad  rem,  168 ;  ad  liomi- 
nem,  168  ;  adpopiihim,  169  ;  ad  igiio- 
raiitiam,  169;    ad  verccundiam,  170, 

Aristotle,  Logic  of,  22  ;  List  of  Logical 
Works,  22;  his  Theory  of  the  Syllo- 
gism, 23;  Importance  of  Induction 
and  Deduction  in  his  Logic,  25 ;  his 
Classification  of  Fallacies,  152;  liis 
Statement  of  the  Law  of  Contradic- 
tion, 295. 

Art,  an,  its  Relation  to  a  Science,  8. 

B 
Bacon,  Logic  of,  28  ;    nis  Method,  28  ; 

on  the  Tendency  to  neglect  Negative 

Instances,  257 ;  his  Idols  of  the  Cave, 

257. 
Bosanquet,  his  Views  of  Logic,  1 1 ,  note ; 

his  Writings  on  Modern   Logic,   17 ; 

his  Remarks  on  Analogy,  227. 
Bradley,  12. 


Cant  Words  and  Phrases,  249. 
Causal  Connection,  Judgments  of,  307. 


Cause,  the  Fallacy  of  the  False,  171; 

the  Development  of  the  Principle  of, 

309. 
Causes,  the  Plurality  of,  204. 
Chances,  the  Calculation  of,  194. 
Circle,  Argument  in  a,  165. 
Classification,  Principles  of,  74;    Rules 

of,  76;  of  Fallacies,  152,  246;   Aris- 
totle's, of  Fallacies,  152. 
Composition,  the  Fallacy  of,  160. 
Concej^ts  and  Judgments,  268. 
Conclusion,  the  Irrelevant,  168. 
Concrete,   two   Senses   of   the   Word, 

51- 
Consequent,  Fallacy  of  the,  170. 
Conservation  of  Energy,  the  Law  of, 

and  its  Influence  on  the  Conception 

of  Cause,  313. 
Contradiction,  the  Law  of,  38,  295. 
Conversion,  the,  of  Propositions,  100; 

Simple,    loi ;     by    Limitation,    loi ; 

by  Contraposition,  102;    Errors  in, 

155- 

D 

Darwin,  his  Power  of  arresting  Ex- 
ceptions, 217;  his  Use  of  Analogy, 
225  ;  his  Employment  of  Hynotheses, 
232. 

Deduction,  its  Relation  to  Induction, 
329- 

Definition,  the  Necessity  of,  63 ;  Verbal 
and  Real,  63;  Ways  of  Regarding, 
64  ;  Socrates'  Searcli  for,  65  ;  Rules 
of,  69. 

Descartes,  29,  335. 

Dialectic,  Socrates'  Use  of,  65, 

Dicliotoniy,  72. 

Difference,  Method  of,  205. 

Differentia,  68. 

Dilemma,  the  ;.i;nple  Constructive,  149  ; 
the  Complex  Constructive,  150;  the 
Complex  Destructive,  150. 


389 


I    •     1 


390 


INDEX 


ijjf:  il 


=5 


Division,  Rules  for,  76;  the  Fallacy  of,  ' 
162. 

E 

Empiricism,  tliu  Doctrine  of,  337. 

I'^nthymemes,  41,  126. 

Enumeration,  as  the  Starting-jioint  of 
Induction,  185;    Judgments  of,  305. 

Episyllogisms  and  I'rosyllogisms,  127. 

Ecjuivoeation,  the  Fallacies  of,  159. 

Ethics,  its  Standpoint  compared  witli  ' 
that  of  Psychology,  316. 

Euler,  no. 

Evolution,  tlie  I^aw  of,  262;  the  Appli- 
cation of  the  Law  of,  to  Thought,  264. 

Excluded   Middle,  the  Law  of,  72,  297. 

Experiment     and     Observation,    180; 
Advantages  of  employing,  180. 

Exjjlanation  and  Observation,  177  ;  the 
Problem  of,  182. 

Extension  and  Intension  of  Terms,  55.  , 


Fallacies,  Classification  of,  152,  246; 
Syllogistic,  149  ;  Inductive,  245  ;  the 
Source  of,  245;  of  Interpretation, 
154 ;  occasioned  by  Language,  246  ; 
of  Reasoning,  157,  254  ;  of  Observa-  j 
tion,  250;    Individual,  257.  | 

Figures   of    the   Syllogism,    113;     the 
Special  Canons  of  the  four,  117  ;  De-  | 
termination  of  the  Valid  Moods  in,  ' 
120;  tlie  Perfect,  123;  tlie  Imperfect,  '.. 
123 ;  Reduction  of,  123  ;  the  Organic 
Relation  of,  125,  note. 


Galen,  123. 

Generalization,  Danger  of  hasty,  256. 
Genus,  its  Definition,  68. 
Guericke,  239. 

H 

Ilegel,  Quotation  from  his  Logic,  11; 
Ills  Influence  on  the  Development  of 
Logic,  31. 

Herschel,  J.,  30. 

Hypothesis,  Reasoning  from  an,  230; 
the  Employment  of,  to  explain  Com- 
mon Events,  231;    Darwin's  Use  of, 


232 ;  the  Necessity  for  an,  233 ; 
Formation  of,  234 ;  the  Function  of 
Analogy  in  suggesting,  223,  236;  tlie 
Proof  of,  237 ;  Requirements  of  a 
Good,  240. 

I 

Identity,  the  Law  of,  38,  288;  Jc- 
vons's  Interpretation  of  the  Law  of, 
289. 

/•'■//('/•(///'i'  lilcitchi,  166. 

Imagination,  its  Part  in  the  F'ormation 
of  Theories,  234. 

Individuality,  Judgments  of,  315. 

Induciion  and  Deiluction,  2,  24,  329; 
the  Baconian  Method  of,  28  ;  Mill's 
Emphasis  on,  31;  the  Problem  of, 
172;   Perfect  and  Imperfect,  187. 

Inference,  Mediate  and  Inuuediate,  92; 
the  Nature  of,  324;  as  distinguished 
from  Judgment,  318;  the  Paradox 
of,  325;  as  a  Development  of  judg- 
ment, 32S ;  and  Number  of  Instances, 
344,     (See  also  Reasonmg.) 

Instances,  the  \'alue  of  Numerous,  345. 

Intension  and  Extension  of  Terms,  55. 

Interpretation,  of  Propositions,  92; 
Errors  of,  154;  Judgment  a  Process 
of,  266. 


James,  7. 

Jevons,  his  Account  of  Perfect  Induc- 
tion 187;  his  Calculation  of  Chances, 
195;  his  Interpretation  of  the  Law 
of  Identity,  289;  his  Princii^lo  of  the 
Substitution  of  Similars,  2S9. 

Judgment,  the  Starting-point  of  Know- 
ledge, 266;  as  a  Process  of  Inter- 
pretation, 267;  and  Concept,  268; 
the  Universality  of,  274 ;  the  Neces- 
sity of,  276;  a  priori,  279;  as  involv- 
ing both  Analysis  and  Synthesis, 
279 ;  as  constructing  a  System  of 
Knowledge,  284;  its  Relation  to  In- 
ference, 318. 

Judgments,  of  Quality,  300;  of  Quan- 
tity, 304;  of  Enumeration,  305;  of 
Measure,  305 ;  of  Causal  Connec- 
tion, 307;  of  Individuality,  315. 


isify  for  an,  233; 
4 ;  the  P'unction  of 
sting,  223,  236;  the 
Requirements   of  a 


of,    38,    288;     je- 
tion  of  the  Law  of, 

[66. 

rt  in  the  Formation 

iiients  of,  315. 
:duction,  2,  24,  329; 
ethod  of,  28  ;   Mill's 
[ ;    the  rrobleni  of, 

Imperfect,  187. 
and  Immediate,  92; 
4 ;    as  distinguished 

318 ;  the  Paradox 
velopment  of  ludg- 
[umber  of  Instances, 
Reasoning.) 
e  of  Numerous,  345. 
insion  of  Terms,  55. 
I'ropositions,  92; 
Judgment  a  Process 


J 


lit  of  Perfect  Induc- 
culation  of  Chances, 
etation  of  the  Law 

iiis  Principle  of  the 
iimilars,  289. 
ting-point  of  Know- 
a   Process  of  Inter- 

and  Concept,  268 ; 
of,  274;  the  Neces- 
/('/■/,  279 ;  as  involv- 
'sis  and  Synthesis, 
icting  a  System  of 
;    its  Relation  to  In- 

iility,  300;  of  Quan- 
mmeration,  305 ;  of 
of  Causal  Connec- 
lividuality,  315. 


INDEX 


391 


l\ 


Ladd,  7. 

Language,  Dangers  from  the  Careless 
Use  of,  61 ;  Fallacies  of,  246 ;  Figura- 
tive, 249. 

Law,  of  Identify,  38,  288;  of  Cuntni- 
(Hction,  38,  295  ;  of  Excluded  Mid- 
dle, 72,  297;  of  Conservation  of 
Energy,  313. 

Laws  of  Thought,  38,  72,  288. 

Locke,  as  the  Representative  of  Imu- 
puicism,  30,  335;  on  the  Careless 
Use  of  Words,  61,  247. 

Logic,  Definition  of,  i;  Derivation  of 
the  Word,  3;  Relation  to  Psychol- 
ogy, 4 ;  Comparison  with  Physio'ogy, 
6;  as  a  Science  and  an  Art,  8  ;  Util- 
ity of,  10;  Necessity  of,  12;  the 
Materials  of,  13  ;  of  the  Sophists,  18  ; 
of  Socrates,  19;  of  Aristotle,  22,  32; 
of  the  Schoolmen,  26;  of  Bacon,  28  ; 
Development  of  Modern,  31  ;  the 
Equational,  289. 

Lyell,  his  Overthrow  of  the  '  Catas- 
trophic' Theory  in  Geology,  243. 

M 

Malthus,  his  Theories  of  Population, 

168,  225, 
Measure,  judgments  of,  305. 
Mental  Operations,  proposed  Division 

of,  43- 

Metaphors,  Dangers  from  the  Use  of, 
250. 

Method,  the  Progressive  or  Synthetic, 
128  ;  the  Regressive  or  Analytic,  128  ; 
the,  of  Agreement,  200;  the,  of  Dif- 
ference, 205;  the  Joint,  of  Agreement 
ami  Difference,  209;  the,  of  Con- 
comitant Variations,  211;  the,  of 
Residues,  213. 

Middle  Term,  the  Function  of  the,  106; 
Ambiguous,  160. 

Mill,  his  Importance  in  the  History  of 
Logic,  30;  his  Experimental  Meth- 
ods, 198  ;  his  View  of  the  Nature  of 
General  Principles,  339;  his  Doc- 
trine that  all  Reasoning  is  from  one 
Particular  Case  to  another,  340. 


Morplioldgv,  compared  with  Psychol- 
ogy, sI '  ■ 

N 

Negative  Instances,  Tendency  to  neg- 
lect, 251. 
Neptune,  the  Discovery  of,  217. 
Newton,  his  Care  in  testing  Tlieories, 

239. 
A'o/t  scqiiifnr,  170. 

O 

Observation,    and    Explanation,    177; 

and    lOxperiment,     i3o;     I'arois    of, 

250. 
Obversion,   the,    of    Propositions,    98; 

Errors  in,  155. 
Opposition,  the,  of  Propositions,  94. 

P 

Perception,  as  involving  Judgment, 
266;  Difficulty  in  distinguishing  be- 
tween Inference  and,  253. 

Petitio  I'riucipii,  165. 

Physiology  compared  with  Logic,  6. 

Plato,  in  the  History  of  Logic,  22;  and 
the  Doctrine  of  Reminiscence,  325. 

Post  hoc  propti'r  hoc,  171,  255. 

Predicables,  the,  67, 

Prejudices,  Individual,  257  ;  of  an  Age, 
258. 

Premises,  Definition  of,  40. 

Presumption,  Fallacies  of,  164. 

ProposiUons,  Categorical,  79;  Condi- 
tional, 79  ;  the  Nature  of,  78  ;  Qual- 
ity and  Quantity  of,  80;  Difficul- 
ties in  classifying,  83 ;  Relation  of 
Subject  and  Predicate  in,  85 ;  the 
Opposition  of,  94;  the  Obversion  of, 
98  ;  the  Conversion  of,  100. 

Psychology,  its  Relation  to  Logic,  4; 
Comparison  with  Morphology,  6; 
Comparison  with  Ethics,  316. 

Q 

Quality,  of  Propositions,  80;  judg- 
ments of,  300. 

Quantity,  of  Propositions,  80;  judg- 
ments  of,  304. 

Quale)  nio  Jcniiiiionoii,  158. 


392 


INDEX 


Question,  the  Fallacy  of  the  Complex, 

166. 
Question-Begging  Epitiiet,  248. 

R 

Rationalism,  its  Point  of  View,  335; 
the  Nature  of  its  Problems,  336;  its 
Neglect  of  Perception,  337. 

Reasoning,  the  Nature  of  Syllogistic, 
105;  Mediate,  92,  107;  Immediate, 
93;  Mistakes  in,  254  ;  Inductive  and 
Deductive,  329 ;  from  P.iriiculars  to 
Particulars,  340 ;  from  Particulars  to 
a  IJn  versa],  344.  (See  also  Infer- 
ence.) 

Reduction  of  the  Imperfect  Figures, 
123. 

Residues,  the  Method  of,  213. 


Schonbein,  his  Discovery  of  Ozone, 
217. 

Science,  as  related  to  Art,  8. 

Sigwart,  on  the  Difference  between 
Ancient  and  Modern  Science,  190; 
on  the  Application  of  Statistics,  191. 

Similars,  the  Principle  of  the  Substitu- 
tion of,  289. 

Socrates,  his  Sense  of  Ignorance,  4;  his 
Place  in  the  History  of  Logic,  20; 
his  Search  for  Definitions,  65 ;  his 
Employment  of  Dialectic,  66. 

Sophists,  the  Logic  of,  19 ;  Socrates' 
Refutation  of,   20;    Plato's  Criticism 


of  their  Theory  of  Knowledge,  22; 
their  .Scepticism,  275. 
Sorites,   Aristotelian,   131 ;    Goclenian, 

131- 

Species,  Definition,  68. 

Spinoza,  as  a  Rationalist,  336. 

Statistics,  189. 

Stout,  7. 

Subject,  Relation  of  Predicate  and,  85. 

Syllogism,  the  Aristotelian,  23,  32;  the 
N.iture  of  the,  36;  the  Principle  of 
the,  38;  the  Parts  of  the,  39;  the 
Rules  of  the,  103  ;  the  Figures  of  the, 
113  ;  the  Hypothetical,  136;  Rules  for 
llie  Hyi)othetical,  137;  Relation  of 
Categorical  and  Hypothetical,  139; 
the  l)isjunctive,  145  ;  Fallacies  of  the 
Disjunctive,  148. 

Synthesis,  its  Relation  to  Analysis,  279. 

System,  Difference  between  a,  and  an 
Aggregate,  285. 


Thales,  310. 

Thought,  the  Laws  of,  38;   the  Nature 

of,  260. 
Tcrriculli,  238. 

V 

V'^ariations,     of    Statistics,     193;     the 
Method  of  Concomitant,  211. 

W 

Whcwell,  15,  30. 
[  Words,  the  Abuse  of,  61,  246. 


of  Knowledge,  22; 

,  275- 

in,  131;    Goclenian, 

1,68. 
ionalist,  336. 


of  Predicate  and,  85. 
istotelian,  23,  32;  the 
36;  the  Principle  of 
'arts  of  the.  39;  the 
3  ;  the  Figures  of  the, 
helical,  136;  Rules  for 
;al,  137;  Relation  of 
d  Hypothetical,  139; 
,  145  •   l'";illacies  of  the 

8. 

ation  to  Analysis,  279. 

ce  between  a,  and  an 


Lws  of,  38  i   the  Nature 


Statistics,     193 ".     ^^" 
)nconiitant,  211. 

W 

), 

use  of,  61,  246. 


A   SUGGESTIVE   BOOK   FOR   TEACHERS. 


The   Education   of   the   Central 
Nervous   System* 

A    STUDY  OF  rOUNDATlOXS,   ESPECIAI.I.Y  OF  SENSORY 
AND   MOTOR    TRAINLXG. 

BY 
REUBEN   POST    HALLECK,    M.A., 

Autiior   of   "  I'sycliology    and    I'sycliic    CiihurL-." 

i2mo.     Cloth.     Price  $1.00,   Net. 


COMMENTS. 


"I  read  with  a  great  deal  of  care  Ilalleck's  *  Education  of  the  Central 
Nervous  System.'  He  has  succeeded  admirably  in  i)rcsenting  the  subject 
in  a  simple,  clear,  logical  way.  It  is  just  the  book,  it  seems  to  me,  for  the 
reading  of  all  persons  interested  in  '  Child  Study.'  "  —  Kka.ncis  W.  Pakkkk, 
Principal  C/iiiago  Normal  School. 

"  Your  elaboration  of  the  idea  that  the  nervous  system  is  to  be  trained  by 
the  separate  practice  of  the  several  senses,  cannot  fail  to  be  suggestive  and 
helpful.  Your  chapter  on  Shakespeare  will  be  of  value,  not  t)nly  from  the 
educational  standpoint,  but  also  to  the  general  student  of  Literature,  who 
has  still  to  recogni/.e  that  Literature  is  an  echo  of  human  sensation,  and 
that  it  is  desirable  for  the  student  to  be  cultivated,  in  order  to  appreciate 
that  field  of  learning."  —  Dr.  II.  C.  DuNALDSON,  Head  Professor  of  Neu- 
rology, Vuii'ersity  of  Chicago. 

"It  is  difficult  to  praise  Ilalleck's  '  Education  of  tlie  Central  Nervous 
System'  too  highly,  for  though  one  may  come  across  many  volumes  written 
with  the  same  purpose,  few,  unhappily,  are  likely  to  do  so  nmch  good."  — 
Yale  Scientific  Monthly. 

"  I  regard  Ilalleck's  '  Education  of  the  Central  Nervous  System  '  as  one 
of  the  most  valuable  contributions  to  the  science  of  jiedagogics  that  I  have 
read.  The  book  ought  to  be  read  by  every  thinking  teacher."  —  B.  I>. 
Hun  TOON,  A.Td.,  Superintenilent  Ky.  Institution  for  the  Education  of  the 
Blind. 


THE    MACMILLAN    COMPANY, 

66   FIFTH  AVENUE,    NEW  YORK. 


Primer   of   Psychology^ 


BY 


EDWARD  BRADFORD  TITCHENER, 

Cornell   riiivcrhity. 


12mo.     Cloth.     Price  $1.00,   Net. 


H 


:(  I 


1 

1 

'■        .     i 

■  ,     6 

! 

1                    ( 

,  hj  ^ 

) 

'I'liK  I'ki.mkr  OF  I'sv(H()I,(h;v  includes  chapters  on  Psychology  : 
What  it  Is  and  What  it  Docs;  Method  of  Psychology;  Sensa- 
tion ;  Affection  and  Feeling  ;  Attention  ;  Perception  ;  Idea  ami 
Association  of  Ideas;  lunotion  ;  The  Simpler  Forms  of  Action  ; 
Memory  and  Imagination ;  Thought  and  Self-Consciousness  ; 
Sentiment ;  The  ('omplex  I'\)rms  of  Action  ;  Abnormal  Psy- 
chology ;  The  Province  and  the  Relations  of  Psychology. 

COMMENTS. 

"  It  is  a  clear  ami  coinin-chcnsivL"  manual  for  the  hcf^inncr."  —  Miss  A.  K. 
WvCKori',  rtu/cer  Itistilntc. 

"it  is  an  excellent  class  book  for  beginners  in  that  branch."  —  A.  J. 
1)A\  IS,  I'yiiicipal  Stale  Xormal,  Clarion,  Pa. 

"  It  <^ives  the  result  of  the  latest  psychological  investigation  in  a  simple 
way,  with  alnimiant  and  apt  illustrations."  —  II.  \V.  McKnkjht,  Pe)uisyl- 
vania  College. 

'•  I  consider  it  admirably  fitted  for  an  introduction  to  the  science,  and  I 
shall  make  it  the  basis  of  my  elementary  instruction  next  year.  It  is  the 
best  primer  of  Psychology  that  I  am  acquainted  with."  —  J.  A.  Leighton, 
Hohart  College. 

"  It  is,  I  believe,  sound,  in  its  teaching,  and  well  adapted  to  class-room 
purposes."  —  J.  A.  Pkti;ks,  Heidelbeyg  Universily.    . 


THE    MACMILLAN    COMPANY, 

66   FIFTH   AVENUE,  NEW   YORK. 


^■■.■JS'.., 


3*»^  •*  ..i"^  OK**  "•!  " 


I  I'sychology  : 
ology  ;  Scnsa- 
ion  ;  Idea  ami 
rms  of  Action  ; 
Consciousness  ; 
U)normal  I'sy- 
•chology. 


icr, 


"  —  Miss  A.  K 


)ranch."  — A.  J- 

ration  in  a  simple 
KNiGiri',  Pennsyl- 

thc  science,  and  I 
t  year.     It  is  the 

-J.  A.  I.EIGHTON, 

,tc(l  to  class-room 


t  t 


\}' 


v> 


An   Outline   of   Psychology^ 


liV 


EDWARD  BRADFORD  TITCHENER, 

(.  oriicll   L'nivci^ity. 


SKCOXI)  EDiriOX,   \V1  III  coKKi:crio.\'S. 


8vo.     Cloth.     $1.50.   Net. 


COMMENTS. 

"As  n  coiittihiitidii  hoth  ahlc  aiul  umjIuI,  I'tufcssnr  'I'itcliciu  r's  vdliimu  will  iimniestion- 
ahly  liiid,  as  H  deserves,  a  iiinsl  cmilial  wclinme.  In  many  ways  it  is  llic  most  scrviLcablc 
tcxt-hodk  of  itsychuliiuy,  fruiii  a  iiunlcni  si-ieiitilK:  (loiiit  of  view,  that  has  hccii  written. 
The  author  is  an  experiiueutalist,  hut  eliiiijs  to  the  spei  ial  iuterpretaliou  of  certain  funda- 
mental principles  whii  ii  is  characteristic  of  W'undt  and  his  ilis.  ipies.  The  result  of  this 
definite  position  is  to  make  the  work  clear,  exact  in  expression,  systematic,  methodical. 
The  work  is  tlu)rouj;hly  t;ood  and  useful."  Jnsiiiii  J.\si  i^ow  ,  University  cf  Wisconsin, 
in  the  I ''in  I. 

"  I'rofessor  Titchener's  work  is  an  able  presentation  of  psychology  viewcil  from  the 
experimental  standpoint.  The  analysis  is  sharp  and  ihuinu.;h,  ami  iu  this  respect  the 
book  will  he  of  value  to  every  '  school  '  As  a  te.\l-hook  it  has  a  l.ujje  field  before  it,  and 
we  may  hope,  besides,  that  it  will  find  its  way  into  the  hands  of  the  '  laity,'  and  help  to 
dispel  some  of  the  grotestjiie  notions  that  are  prevalent  about  exjieriinental  psychology." 
—  H.  C.  Wakukn,  Princeton  University,  in  /'syc/io/oi/iciii  A\-;'ie:o. 

"This  book  is  one  of  the  best  of  recent  outli.  cs  of  psycholotjy.  It  is  mm  h  belter  bal- 
anced and  more  symmetrically  conceived  than  any  other  e.xisling  book  on  the  subject.  'I'lie 
work  can  certainly  be  refonunended  as  one  of  the  best  and  most  representative  text-books 
on  the  psychology  of  the  present  day.  It  is  a  book  which  every  teacher  and  every  student 
of  psychology  who  wishes  to  become  f.imiliar  with  modern  psychology  can  be  recom- 
mended to  study."  -    7'/ie  Teacher. 

"The  Outline  of  Psychology  is  written  with  admir.d)le  i  learness.  The  results  of 
experimental  psychology  are  expounded  in  a  style  both  attractive  and  simple.  The 
characteristics  of  the  book  that  are  to  be  most  highly  coniuieuded  are  clearness,  simplicity, 
wealth  of  illustration,  ami,  in  general,  atlaptation  to  tlie  needs  of  the  beginner  who  requires 
to  be  placed  en  rapport  with  the  latest  residts  of  experimental  psychology."  —  X'ltnre. 


'ANY, 
Irk. 


THE    MACMILLAN   COMPANY, 

66   FIFTH   AVENUE,    NEW   YORK. 


The   Meaning   of   Education^ 

AM)  (»rnKK 
ESSAYS   AND   ADDRESSES. 


* 
I 


HY 


■^^J 


I* 


k>i 


'    II 


-   ii 


If 

■         i 

r  1 

1    H 

I 

1 

;1 

i  '    l^l 

NICHOLAS  MURRAY  BUTLER, 

Prnfcsiijr  of  Philusophy  and  Eilucntion  in  Culutnbia  University. 


12mo.     Cloth.     230  pages.     $1.00. 


The  other  papers  included  in  the  volume  are : 

What  Knowlkih;!',  is  Most  W(M<th? 

Is  there  a  New  Education? 

Democracy  and  Education. 

The  American  College  and  the  American  University. 

The  Function  of  the  Secondary  School. 

The  Reform  of  Secondary  Education  in  the  United  States. 


In  these  essays  and  addresses  Professor  Butler  offers  a  con- 
tribution to  educational  theory  by  basing  the  process  of  educa- 
tion upon  the  facts  of  organic  evolution,  an c^^^)ro posing  a 
standard  for  the  measurement  of  educational^^^^uideduca- 
tional  effectiveness.  It  is  the  belief  of  the  autffl^P^^Bftsed 
in  his  Introduction,  that  it  is  possible  to  deal  with  alFof  the 
questions  discussed  in  a  scient'^'^  spirit  and  by  a  scientific 
method.  The  book  is  not  intended  for  teachers  alone,  but  for 
parents  and  for  all  persons  interested  in  education. 


For  further  information  please  address 

THE    MACMILLAN   COMPANY, 

66   FIFTH   AVENUE,   NE^A^  YORK. 


:ation; 


rnivcrsity. 


are: 


niversity. 
United  States. 


Vfr 


ir  offers  a  con- 
)cess  of  educa- 
)roposing  a 
educa- 
ed 

with  alTof  the 
by  a  scientific 
alone,  but  for 
in. 


S 


^ 


ANY, 


v#:;-^;w<  <■.**■'¥•■■ 


^-..fc;.i.«(*r-s,*«,-:j.. 


